New order #4: World












16












$begingroup$


Introduction (may be ignored)



Putting all positive numbers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all positive numbers. This is the fourth challenge in this series (links to the first, second and third challenge).



In this challenge, we will explore not one permutation of the natural numbers, but an entire world of permutations!



In 2000, Clark Kimberling posed a problem in the 26th issue of Crux Mathematicorum, a scientific journal of mathematics published by the Canadian Mathematical Society. The problem was:




$text{Sequence }a = begin{cases}
a_1 = 1\
a_n = lfloor frac{a_{n-1}}{2} rfloortext{ if }lfloor frac{a_{n-1}}{2} rfloor notin {0, a_1, ... , a_{n-1}}\
a_n = 3 a_{n-1}text{ otherwise}
end{cases}$



Does every positive integer occur exactly once in this sequence?




In 2004, Mateusz Kwasnicki provided positive proof in the same journal and in 2008, he published a more formal and (compared to the original question) a more general proof. He formulated the sequence with parameters $p$ and $q$:



$begin{cases}
a_1 = 1\
a_n = lfloor frac{a_{n-1}}{q} rfloortext{ if }lfloor frac{a_{n-1}}{q} rfloor notin {0, a_1, ... , a_{n-1}}\
a_n = p a_{n-1}text{ otherwise}
end{cases}$



He proved that for any $p, q>1$ such that $log_p(q)$ is irrational, the sequence is a permutation of the natural numbers. Since there are an infinite number of $p$ and $q$ values for which this is true, this is truly an entire world of permutations of the natural numbers. We will stick with the original $(p, q)=(3, 2)$, and for these paramters, the sequence can be found as A050000 in the OEIS. Its first 20 elements are:



1, 3, 9, 4, 2, 6, 18, 54, 27, 13, 39, 19, 57, 28, 14, 7, 21, 10, 5, 15


Since this is a "pure sequence" challenge, the task is to output $a(n)$ for a given $n$ as input, where $a(n)$ is A050000.



Task



Given an integer input $n$, output $a(n)$ in integer format, where:



$begin{cases}
a(1) = 1\
a(n) = lfloor frac{a(n-1)}{2} rfloortext{ if }lfloor frac{a(n-1)}{2} rfloor notin {0, a_1, ... , a(n-1)}\
a(n) = 3 a(n-1)text{ otherwise}
end{cases}$



Note: 1-based indexing is assumed here; you may use 0-based indexing, so $a(0) = 1; a(1) = 3$, etc. Please mention this in your answer if you choose to use this.



Test cases



Input | Output
---------------
1 | 1
5 | 2
20 | 15
50 | 165
78 | 207
123 | 94
1234 | 3537
3000 | 2245
9999 | 4065
29890 | 149853


Rules




  • Input and output are integers (your program should at least support input and output in the range of 1 up to 32767)

  • Invalid input (0, floats, strings, negative values, etc.) may lead to unpredicted output, errors or (un)defined behaviour.

  • Default I/O rules apply.


  • Default loopholes are forbidden.

  • This is code-golf, so the shortest answers in bytes wins










share|improve this question











$endgroup$












  • $begingroup$
    Sharp! My mistake. Corrected it. Sorry if this caused any trouble or confusion.
    $endgroup$
    – agtoever
    yesterday


















16












$begingroup$


Introduction (may be ignored)



Putting all positive numbers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all positive numbers. This is the fourth challenge in this series (links to the first, second and third challenge).



In this challenge, we will explore not one permutation of the natural numbers, but an entire world of permutations!



In 2000, Clark Kimberling posed a problem in the 26th issue of Crux Mathematicorum, a scientific journal of mathematics published by the Canadian Mathematical Society. The problem was:




$text{Sequence }a = begin{cases}
a_1 = 1\
a_n = lfloor frac{a_{n-1}}{2} rfloortext{ if }lfloor frac{a_{n-1}}{2} rfloor notin {0, a_1, ... , a_{n-1}}\
a_n = 3 a_{n-1}text{ otherwise}
end{cases}$



Does every positive integer occur exactly once in this sequence?




In 2004, Mateusz Kwasnicki provided positive proof in the same journal and in 2008, he published a more formal and (compared to the original question) a more general proof. He formulated the sequence with parameters $p$ and $q$:



$begin{cases}
a_1 = 1\
a_n = lfloor frac{a_{n-1}}{q} rfloortext{ if }lfloor frac{a_{n-1}}{q} rfloor notin {0, a_1, ... , a_{n-1}}\
a_n = p a_{n-1}text{ otherwise}
end{cases}$



He proved that for any $p, q>1$ such that $log_p(q)$ is irrational, the sequence is a permutation of the natural numbers. Since there are an infinite number of $p$ and $q$ values for which this is true, this is truly an entire world of permutations of the natural numbers. We will stick with the original $(p, q)=(3, 2)$, and for these paramters, the sequence can be found as A050000 in the OEIS. Its first 20 elements are:



1, 3, 9, 4, 2, 6, 18, 54, 27, 13, 39, 19, 57, 28, 14, 7, 21, 10, 5, 15


Since this is a "pure sequence" challenge, the task is to output $a(n)$ for a given $n$ as input, where $a(n)$ is A050000.



Task



Given an integer input $n$, output $a(n)$ in integer format, where:



$begin{cases}
a(1) = 1\
a(n) = lfloor frac{a(n-1)}{2} rfloortext{ if }lfloor frac{a(n-1)}{2} rfloor notin {0, a_1, ... , a(n-1)}\
a(n) = 3 a(n-1)text{ otherwise}
end{cases}$



Note: 1-based indexing is assumed here; you may use 0-based indexing, so $a(0) = 1; a(1) = 3$, etc. Please mention this in your answer if you choose to use this.



Test cases



Input | Output
---------------
1 | 1
5 | 2
20 | 15
50 | 165
78 | 207
123 | 94
1234 | 3537
3000 | 2245
9999 | 4065
29890 | 149853


Rules




  • Input and output are integers (your program should at least support input and output in the range of 1 up to 32767)

  • Invalid input (0, floats, strings, negative values, etc.) may lead to unpredicted output, errors or (un)defined behaviour.

  • Default I/O rules apply.


  • Default loopholes are forbidden.

  • This is code-golf, so the shortest answers in bytes wins










share|improve this question











$endgroup$












  • $begingroup$
    Sharp! My mistake. Corrected it. Sorry if this caused any trouble or confusion.
    $endgroup$
    – agtoever
    yesterday
















16












16








16





$begingroup$


Introduction (may be ignored)



Putting all positive numbers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all positive numbers. This is the fourth challenge in this series (links to the first, second and third challenge).



In this challenge, we will explore not one permutation of the natural numbers, but an entire world of permutations!



In 2000, Clark Kimberling posed a problem in the 26th issue of Crux Mathematicorum, a scientific journal of mathematics published by the Canadian Mathematical Society. The problem was:




$text{Sequence }a = begin{cases}
a_1 = 1\
a_n = lfloor frac{a_{n-1}}{2} rfloortext{ if }lfloor frac{a_{n-1}}{2} rfloor notin {0, a_1, ... , a_{n-1}}\
a_n = 3 a_{n-1}text{ otherwise}
end{cases}$



Does every positive integer occur exactly once in this sequence?




In 2004, Mateusz Kwasnicki provided positive proof in the same journal and in 2008, he published a more formal and (compared to the original question) a more general proof. He formulated the sequence with parameters $p$ and $q$:



$begin{cases}
a_1 = 1\
a_n = lfloor frac{a_{n-1}}{q} rfloortext{ if }lfloor frac{a_{n-1}}{q} rfloor notin {0, a_1, ... , a_{n-1}}\
a_n = p a_{n-1}text{ otherwise}
end{cases}$



He proved that for any $p, q>1$ such that $log_p(q)$ is irrational, the sequence is a permutation of the natural numbers. Since there are an infinite number of $p$ and $q$ values for which this is true, this is truly an entire world of permutations of the natural numbers. We will stick with the original $(p, q)=(3, 2)$, and for these paramters, the sequence can be found as A050000 in the OEIS. Its first 20 elements are:



1, 3, 9, 4, 2, 6, 18, 54, 27, 13, 39, 19, 57, 28, 14, 7, 21, 10, 5, 15


Since this is a "pure sequence" challenge, the task is to output $a(n)$ for a given $n$ as input, where $a(n)$ is A050000.



Task



Given an integer input $n$, output $a(n)$ in integer format, where:



$begin{cases}
a(1) = 1\
a(n) = lfloor frac{a(n-1)}{2} rfloortext{ if }lfloor frac{a(n-1)}{2} rfloor notin {0, a_1, ... , a(n-1)}\
a(n) = 3 a(n-1)text{ otherwise}
end{cases}$



Note: 1-based indexing is assumed here; you may use 0-based indexing, so $a(0) = 1; a(1) = 3$, etc. Please mention this in your answer if you choose to use this.



Test cases



Input | Output
---------------
1 | 1
5 | 2
20 | 15
50 | 165
78 | 207
123 | 94
1234 | 3537
3000 | 2245
9999 | 4065
29890 | 149853


Rules




  • Input and output are integers (your program should at least support input and output in the range of 1 up to 32767)

  • Invalid input (0, floats, strings, negative values, etc.) may lead to unpredicted output, errors or (un)defined behaviour.

  • Default I/O rules apply.


  • Default loopholes are forbidden.

  • This is code-golf, so the shortest answers in bytes wins










share|improve this question











$endgroup$




Introduction (may be ignored)



Putting all positive numbers in its regular order (1, 2, 3, ...) is a bit boring, isn't it? So here is a series of challenges around permutations (reshuffelings) of all positive numbers. This is the fourth challenge in this series (links to the first, second and third challenge).



In this challenge, we will explore not one permutation of the natural numbers, but an entire world of permutations!



In 2000, Clark Kimberling posed a problem in the 26th issue of Crux Mathematicorum, a scientific journal of mathematics published by the Canadian Mathematical Society. The problem was:




$text{Sequence }a = begin{cases}
a_1 = 1\
a_n = lfloor frac{a_{n-1}}{2} rfloortext{ if }lfloor frac{a_{n-1}}{2} rfloor notin {0, a_1, ... , a_{n-1}}\
a_n = 3 a_{n-1}text{ otherwise}
end{cases}$



Does every positive integer occur exactly once in this sequence?




In 2004, Mateusz Kwasnicki provided positive proof in the same journal and in 2008, he published a more formal and (compared to the original question) a more general proof. He formulated the sequence with parameters $p$ and $q$:



$begin{cases}
a_1 = 1\
a_n = lfloor frac{a_{n-1}}{q} rfloortext{ if }lfloor frac{a_{n-1}}{q} rfloor notin {0, a_1, ... , a_{n-1}}\
a_n = p a_{n-1}text{ otherwise}
end{cases}$



He proved that for any $p, q>1$ such that $log_p(q)$ is irrational, the sequence is a permutation of the natural numbers. Since there are an infinite number of $p$ and $q$ values for which this is true, this is truly an entire world of permutations of the natural numbers. We will stick with the original $(p, q)=(3, 2)$, and for these paramters, the sequence can be found as A050000 in the OEIS. Its first 20 elements are:



1, 3, 9, 4, 2, 6, 18, 54, 27, 13, 39, 19, 57, 28, 14, 7, 21, 10, 5, 15


Since this is a "pure sequence" challenge, the task is to output $a(n)$ for a given $n$ as input, where $a(n)$ is A050000.



Task



Given an integer input $n$, output $a(n)$ in integer format, where:



$begin{cases}
a(1) = 1\
a(n) = lfloor frac{a(n-1)}{2} rfloortext{ if }lfloor frac{a(n-1)}{2} rfloor notin {0, a_1, ... , a(n-1)}\
a(n) = 3 a(n-1)text{ otherwise}
end{cases}$



Note: 1-based indexing is assumed here; you may use 0-based indexing, so $a(0) = 1; a(1) = 3$, etc. Please mention this in your answer if you choose to use this.



Test cases



Input | Output
---------------
1 | 1
5 | 2
20 | 15
50 | 165
78 | 207
123 | 94
1234 | 3537
3000 | 2245
9999 | 4065
29890 | 149853


Rules




  • Input and output are integers (your program should at least support input and output in the range of 1 up to 32767)

  • Invalid input (0, floats, strings, negative values, etc.) may lead to unpredicted output, errors or (un)defined behaviour.

  • Default I/O rules apply.


  • Default loopholes are forbidden.

  • This is code-golf, so the shortest answers in bytes wins







code-golf sequence






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edited yesterday







agtoever

















asked yesterday









agtoeveragtoever

1,322424




1,322424












  • $begingroup$
    Sharp! My mistake. Corrected it. Sorry if this caused any trouble or confusion.
    $endgroup$
    – agtoever
    yesterday




















  • $begingroup$
    Sharp! My mistake. Corrected it. Sorry if this caused any trouble or confusion.
    $endgroup$
    – agtoever
    yesterday


















$begingroup$
Sharp! My mistake. Corrected it. Sorry if this caused any trouble or confusion.
$endgroup$
– agtoever
yesterday






$begingroup$
Sharp! My mistake. Corrected it. Sorry if this caused any trouble or confusion.
$endgroup$
– agtoever
yesterday












18 Answers
18






active

oldest

votes


















5












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Jelly, 15 bytes



µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ


A full program accepting the integer, n (1-based), from STDIN which prints the result.



Try it online!



How?



µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ - Main Link: no arguments (implicit left argument = 0)
µ µ¡ - repeat this monadic chain STDIN times (starting with x=0)
- e.g. x = ... 0 [1,0] [9,3,1,0]
×3 - multiply by 3 0 [3,0] [27,9,3,0]
H - halve 0 [1.5,0] [4.5,1.5,0.5,0]
ż - zip together [0,0] [[3,1.5],[0,0]] [[27,4.5],[9,1.5],[3,0.5],[0,0]]
Ḟ - floor [0,0] [[3,1],[0,0]] [[27,4],[9,1],[3,0],[0,0]]
Ḣ - head 0 [3,1] [27,4]
ḟ - filter discard if in x [3] [27,4]
ȯ1 - logical OR with 1 1 [3] [27,4]
Ṫ - tail 1 3 4
; - concatenate with x [1,0] [3,1,0] [4,9,3,1,0]
Ḣ - head 1 3 4
- implicit print





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    5












    $begingroup$

    JavaScript (ES6),  55 51  50 bytes



    Saved 1 byte thanks to @EmbodimentofIgnorance
    Saved 1 byte thanks to @tsh





    n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")


    Try it online!






    share|improve this answer











    $endgroup$













    • $begingroup$
      55 bytes
      $endgroup$
      – Embodiment of Ignorance
      yesterday












    • $begingroup$
      @EmbodimentofIgnorance I usually avoid that trick, as the eval'ed code is much slower. But the difference is barely noticeable for that one, so I guess that's fine.
      $endgroup$
      – Arnauld
      yesterday






    • 1




      $begingroup$
      But this is code-golf, we don't care about speed, as long as it gets the job done
      $endgroup$
      – Embodiment of Ignorance
      yesterday










    • $begingroup$
      n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")
      $endgroup$
      – tsh
      yesterday



















    3












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    Perl 6, 51 bytes





    {(1,3,{first *∉@_,@_[*-1]+>1,3*@_[*-1]}...*)[$_]}


    Try it online!



    Returns the 0-indexed element in the sequence. You can change this to 1-indexed by changing the starting elements to 0,1 instead of 1,3



    Explanation:



    {                                               }  # Anonymous code block
    ( ...*)[$_] # Index into the infinite sequence
    1,3 # That starts with 1,3
    ,{ } # And each element is
    first # The first of
    @_[*-1]+>1 # The previous element bitshifted one
    ,3*@_[*-1] # Triple the previous element
    *∉@_, # That hasn't appeared in the sequence





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      3












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      J, 47 40 bytes



      [:{:0 1(],<.@-:@{:@](e.{[,3*{:@])])^:[~]


      Try it online!



      ungolfed



      [: {: 0 1 (] , <.@-:@{:@] (e. { [ , 3 * {:@]) ])^:[~ ]


      Direct translation of the definition into J. It builds bottom up by using ^: to iterate from the starting value the required number of times.






      share|improve this answer











      $endgroup$





















        3












        $begingroup$


        05AB1E, 16 15 bytes



        Saved 1 byte thanks to Kevin Cruijssen.

        0-indexed.



        ¾ˆ$FDˆx3*‚;ï¯Kн


        Try it online!



        Explanation



        Using n=1 as example



        ¾ˆ                 # initialize global array as [0]
        $ # initialize stack with 1, input
        F # input times do:
        Dˆ # duplicate current item (initially 1) and add one copy to global array
        # STACK: 1, GLOBAL_ARRAY: [0, 1]
        x # push Top_of_stack*2
        # STACK: 1, 2, GLOBAL_ARRAY: [0, 1]
        3* # multiply by 3
        # STACK: 1, 6, GLOBAL_ARRAY: [0, 1]
        ‚;ï # pair and integer divide both by 2
        # STACK: [0, 3], GLOBAL_ARRAY: [0, 1]
        ¯K # remove any numbers already in the global array
        # STACK: [3], GLOBAL_ARRAY: [0, 1]
        н # and take the head
        # STACK: 3





        share|improve this answer











        $endgroup$













        • $begingroup$
          15 bytes
          $endgroup$
          – Kevin Cruijssen
          16 hours ago










        • $begingroup$
          @KevinCruijssen: Thanks! I thought of using the global array, but assumed it would be the same length as a list on the stack and never tried it :/
          $endgroup$
          – Emigna
          16 hours ago



















        2












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        Jelly, 21 bytes



        Ø.;0ị×3$:2$:2eɗ?Ɗ$⁸¡Ṫ


        Try it online!



        A monadic link that takes zero-indexed $n$ as the argument and returns $a(n)$.






        share|improve this answer









        $endgroup$





















          2












          $begingroup$

          Java 10, 120 99 bytes





          n->{var L=" 1 0 ";int r=1,t;for(;n-->0;L+=r+" ")if(L.contains(" "+(r=(t=r)/2)+" "))r=t*3;return r;}


          Try it online.



          Explanation:



          n->{                              // Method with integer as both parameter and return-type
          var L=" 1 0 "; // Create a String that acts as 'List', starting at [1,0]
          int r=1, // Result-integer, starting at 1
          t; // Temp-integer, uninitialized
          for(;n-->0; // Loop the input amount of times:
          L+=r+" ")) // After every iteration: add the result to the 'List'
          t=r // Create a copy of the result in `t`
          r=(...)/2 // Then integer-divide the result by 2
          if(L.contains(" "+(...)+" ")) // If the 'List' contains this result//2:
          r=t*3; // Set the result to `t` multiplied by 3 instead
          return r;} // Return the result





          share|improve this answer











          $endgroup$





















            2












            $begingroup$


            Japt, 15 14 bytes



            1-indexed.



            @[X*3Xz]kZ Ì}g


            Try it



            @[X*3Xz]kZ Ì}g     :Implicit input of integer U
            g :Starting with the array [0,1] do the following U times, pushing the result to the array each time
            @ : Pass the last element X in the array Z through the following function
            [ : Build an array containing
            X*3 : X multiplied by 3
            Xz : X floor divided by 2
            ] : Close array
            kZ : Remove all elements contained in Z
            Ì : Get the last element
            } : End function
            :Implicit output of the last element in the array





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              2












              $begingroup$


              Haskell, 67 65 bytes





              (h[1,0]!!)
              h l@(a:o)|elem(div a 2)o=a:h(3*a:l)|1>0=a:h(div a 2:l)


              Try it online!



              Uses 0-based indexing.



              EDIT: saved 2 bytes by using elem instead of notElem and switching conditions






              share|improve this answer











              $endgroup$





















                2












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                Python 2, 66 bytes





                l=lambda n,p=1,s=[0]:p*(n<len(s))or l(n,3*p*(p/2in s)or p/2,[p]+s)


                Try it online!



                Uses zero-based indexing. The lambda does little more than recursively building up the sequence and returning as soon as the required index is reached.






                share|improve this answer









                $endgroup$





















                  1












                  $begingroup$


                  Wolfram Language (Mathematica), 63 bytes



                  (L=Last)@Nest[{##,If[FreeQ[#,x=⌊L@#/2⌋],x,3L@#]}&,{0,1},#]&


                  Try it online!



                  This is 0-indexed

                  (In TIO I added -1 in every test case)






                  share|improve this answer











                  $endgroup$





















                    1












                    $begingroup$


                    Ruby, 54 52 48 bytes





                    ->n{*s=0;j=2;n.times{s<<j=s==s-[j/2]?j/2:j*3};j}


                    Try it online!






                    share|improve this answer











                    $endgroup$





















                      1












                      $begingroup$


                      C++ (gcc), 189 180 bytes



                      -9 bytes to small golfing





                      #import<vector>
                      #import<algorithm>
                      int a(int n){std::vector<int>s={1};for(int i=0;i<n;++i)s.push_back(i&&std::find(s.begin(),s.end(),s[i]/2)==s.end()?s[i]/2:3*s[i]);return s[n-1];}


                      Try it online!



                      Computes the sequence up to n, then returns the desired element. Slow for larger indices.






                      share|improve this answer











                      $endgroup$





















                        1












                        $begingroup$


                        Stax, 14 bytes



                        üÑα↕○Ü1∟¡f↑ô┬♥


                        Run and debug it



                        Zero-indexed.






                        share|improve this answer









                        $endgroup$





















                          1












                          $begingroup$


                          Python 2, 62 bytes





                          a=lambda n:n<1or a(n-1)*6**(a(n-1)//2in[0]+map(a,range(n)))//2


                          Try it online!



                          Returns True for a(0). 0-indexed.






                          share|improve this answer









                          $endgroup$





















                            1












                            $begingroup$


                            Python 3, 105 103 100 95 83 bytes



                            -2 bytes thanks to agtoever
                            -12 bytes thanks to ArBo





                            def f(n):
                            s=0,1
                            while len(s)<=n:t=s[-1]//2;s+=(t in s)*3*s[-1]or t,
                            return s[-1]


                            Try it online!






                            share|improve this answer











                            $endgroup$













                            • $begingroup$
                              You can replace the for loop with while len(s)<=n and replace the i's with -1. This should shave off one of two characters.
                              $endgroup$
                              – agtoever
                              17 hours ago










                            • $begingroup$
                              @agtoever that's so clever - thanks! :)
                              $endgroup$
                              – Noodle9
                              15 hours ago










                            • $begingroup$
                              83 bytes by working with a tuple instead of a list, and removing the if from the while loop to allow one-lining that loop
                              $endgroup$
                              – ArBo
                              9 hours ago












                            • $begingroup$
                              @ArBo wow! absolutely brilliant - thanks :)
                              $endgroup$
                              – Noodle9
                              6 hours ago



















                            1












                            $begingroup$


                            Gaia, 22 20 bytes



                            2…@⟨:):3פḥ⌋,;D)+⟩ₓ)


                            Try it online!



                            0-based index.



                            Credit to Shaggy for the approach



                            2…			| push [0 1]
                            @⟨ ⟩ₓ | do the following n times:
                            :): | dup the list L, take the last element e, and dup that
                            3פḥ⌋, | push [3*e floor(e/2)]
                            ;D | take the asymmetric set difference [3*e floor(e/2)] - L
                            )+ | take the last element of the difference and add it to the end of L (end of loop)
                            ) | finally, take the last element and output it


                            ;D






                            share|improve this answer











                            $endgroup$





















                              0












                              $begingroup$


                              Haskell, 55 bytes





                              (1%[0]!!)
                              a%o|b<-div a 2=a:last(b:[3*a|elem b o])%(a:o)


                              Try it online!



                              Golfing user1472751's slick list-generation method.



                              Same length:





                              (1%[0]!!)
                              a%o=a:[x|x<-[div a 2,a*3],all(/=x)o]!!0%(a:o)


                              Try it online!






                              share|improve this answer











                              $endgroup$














                                Your Answer





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                                18 Answers
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                                5












                                $begingroup$


                                Jelly, 15 bytes



                                µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ


                                A full program accepting the integer, n (1-based), from STDIN which prints the result.



                                Try it online!



                                How?



                                µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ - Main Link: no arguments (implicit left argument = 0)
                                µ µ¡ - repeat this monadic chain STDIN times (starting with x=0)
                                - e.g. x = ... 0 [1,0] [9,3,1,0]
                                ×3 - multiply by 3 0 [3,0] [27,9,3,0]
                                H - halve 0 [1.5,0] [4.5,1.5,0.5,0]
                                ż - zip together [0,0] [[3,1.5],[0,0]] [[27,4.5],[9,1.5],[3,0.5],[0,0]]
                                Ḟ - floor [0,0] [[3,1],[0,0]] [[27,4],[9,1],[3,0],[0,0]]
                                Ḣ - head 0 [3,1] [27,4]
                                ḟ - filter discard if in x [3] [27,4]
                                ȯ1 - logical OR with 1 1 [3] [27,4]
                                Ṫ - tail 1 3 4
                                ; - concatenate with x [1,0] [3,1,0] [4,9,3,1,0]
                                Ḣ - head 1 3 4
                                - implicit print





                                share|improve this answer









                                $endgroup$


















                                  5












                                  $begingroup$


                                  Jelly, 15 bytes



                                  µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ


                                  A full program accepting the integer, n (1-based), from STDIN which prints the result.



                                  Try it online!



                                  How?



                                  µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ - Main Link: no arguments (implicit left argument = 0)
                                  µ µ¡ - repeat this monadic chain STDIN times (starting with x=0)
                                  - e.g. x = ... 0 [1,0] [9,3,1,0]
                                  ×3 - multiply by 3 0 [3,0] [27,9,3,0]
                                  H - halve 0 [1.5,0] [4.5,1.5,0.5,0]
                                  ż - zip together [0,0] [[3,1.5],[0,0]] [[27,4.5],[9,1.5],[3,0.5],[0,0]]
                                  Ḟ - floor [0,0] [[3,1],[0,0]] [[27,4],[9,1],[3,0],[0,0]]
                                  Ḣ - head 0 [3,1] [27,4]
                                  ḟ - filter discard if in x [3] [27,4]
                                  ȯ1 - logical OR with 1 1 [3] [27,4]
                                  Ṫ - tail 1 3 4
                                  ; - concatenate with x [1,0] [3,1,0] [4,9,3,1,0]
                                  Ḣ - head 1 3 4
                                  - implicit print





                                  share|improve this answer









                                  $endgroup$
















                                    5












                                    5








                                    5





                                    $begingroup$


                                    Jelly, 15 bytes



                                    µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ


                                    A full program accepting the integer, n (1-based), from STDIN which prints the result.



                                    Try it online!



                                    How?



                                    µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ - Main Link: no arguments (implicit left argument = 0)
                                    µ µ¡ - repeat this monadic chain STDIN times (starting with x=0)
                                    - e.g. x = ... 0 [1,0] [9,3,1,0]
                                    ×3 - multiply by 3 0 [3,0] [27,9,3,0]
                                    H - halve 0 [1.5,0] [4.5,1.5,0.5,0]
                                    ż - zip together [0,0] [[3,1.5],[0,0]] [[27,4.5],[9,1.5],[3,0.5],[0,0]]
                                    Ḟ - floor [0,0] [[3,1],[0,0]] [[27,4],[9,1],[3,0],[0,0]]
                                    Ḣ - head 0 [3,1] [27,4]
                                    ḟ - filter discard if in x [3] [27,4]
                                    ȯ1 - logical OR with 1 1 [3] [27,4]
                                    Ṫ - tail 1 3 4
                                    ; - concatenate with x [1,0] [3,1,0] [4,9,3,1,0]
                                    Ḣ - head 1 3 4
                                    - implicit print





                                    share|improve this answer









                                    $endgroup$




                                    Jelly, 15 bytes



                                    µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ


                                    A full program accepting the integer, n (1-based), from STDIN which prints the result.



                                    Try it online!



                                    How?



                                    µ×3żHḞḢḟȯ1Ṫ;µ¡Ḣ - Main Link: no arguments (implicit left argument = 0)
                                    µ µ¡ - repeat this monadic chain STDIN times (starting with x=0)
                                    - e.g. x = ... 0 [1,0] [9,3,1,0]
                                    ×3 - multiply by 3 0 [3,0] [27,9,3,0]
                                    H - halve 0 [1.5,0] [4.5,1.5,0.5,0]
                                    ż - zip together [0,0] [[3,1.5],[0,0]] [[27,4.5],[9,1.5],[3,0.5],[0,0]]
                                    Ḟ - floor [0,0] [[3,1],[0,0]] [[27,4],[9,1],[3,0],[0,0]]
                                    Ḣ - head 0 [3,1] [27,4]
                                    ḟ - filter discard if in x [3] [27,4]
                                    ȯ1 - logical OR with 1 1 [3] [27,4]
                                    Ṫ - tail 1 3 4
                                    ; - concatenate with x [1,0] [3,1,0] [4,9,3,1,0]
                                    Ḣ - head 1 3 4
                                    - implicit print






                                    share|improve this answer












                                    share|improve this answer



                                    share|improve this answer










                                    answered yesterday









                                    Jonathan AllanJonathan Allan

                                    54k536174




                                    54k536174























                                        5












                                        $begingroup$

                                        JavaScript (ES6),  55 51  50 bytes



                                        Saved 1 byte thanks to @EmbodimentofIgnorance
                                        Saved 1 byte thanks to @tsh





                                        n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")


                                        Try it online!






                                        share|improve this answer











                                        $endgroup$













                                        • $begingroup$
                                          55 bytes
                                          $endgroup$
                                          – Embodiment of Ignorance
                                          yesterday












                                        • $begingroup$
                                          @EmbodimentofIgnorance I usually avoid that trick, as the eval'ed code is much slower. But the difference is barely noticeable for that one, so I guess that's fine.
                                          $endgroup$
                                          – Arnauld
                                          yesterday






                                        • 1




                                          $begingroup$
                                          But this is code-golf, we don't care about speed, as long as it gets the job done
                                          $endgroup$
                                          – Embodiment of Ignorance
                                          yesterday










                                        • $begingroup$
                                          n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")
                                          $endgroup$
                                          – tsh
                                          yesterday
















                                        5












                                        $begingroup$

                                        JavaScript (ES6),  55 51  50 bytes



                                        Saved 1 byte thanks to @EmbodimentofIgnorance
                                        Saved 1 byte thanks to @tsh





                                        n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")


                                        Try it online!






                                        share|improve this answer











                                        $endgroup$













                                        • $begingroup$
                                          55 bytes
                                          $endgroup$
                                          – Embodiment of Ignorance
                                          yesterday












                                        • $begingroup$
                                          @EmbodimentofIgnorance I usually avoid that trick, as the eval'ed code is much slower. But the difference is barely noticeable for that one, so I guess that's fine.
                                          $endgroup$
                                          – Arnauld
                                          yesterday






                                        • 1




                                          $begingroup$
                                          But this is code-golf, we don't care about speed, as long as it gets the job done
                                          $endgroup$
                                          – Embodiment of Ignorance
                                          yesterday










                                        • $begingroup$
                                          n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")
                                          $endgroup$
                                          – tsh
                                          yesterday














                                        5












                                        5








                                        5





                                        $begingroup$

                                        JavaScript (ES6),  55 51  50 bytes



                                        Saved 1 byte thanks to @EmbodimentofIgnorance
                                        Saved 1 byte thanks to @tsh





                                        n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")


                                        Try it online!






                                        share|improve this answer











                                        $endgroup$



                                        JavaScript (ES6),  55 51  50 bytes



                                        Saved 1 byte thanks to @EmbodimentofIgnorance
                                        Saved 1 byte thanks to @tsh





                                        n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")


                                        Try it online!







                                        share|improve this answer














                                        share|improve this answer



                                        share|improve this answer








                                        edited 20 hours ago

























                                        answered yesterday









                                        ArnauldArnauld

                                        80.6k797334




                                        80.6k797334












                                        • $begingroup$
                                          55 bytes
                                          $endgroup$
                                          – Embodiment of Ignorance
                                          yesterday












                                        • $begingroup$
                                          @EmbodimentofIgnorance I usually avoid that trick, as the eval'ed code is much slower. But the difference is barely noticeable for that one, so I guess that's fine.
                                          $endgroup$
                                          – Arnauld
                                          yesterday






                                        • 1




                                          $begingroup$
                                          But this is code-golf, we don't care about speed, as long as it gets the job done
                                          $endgroup$
                                          – Embodiment of Ignorance
                                          yesterday










                                        • $begingroup$
                                          n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")
                                          $endgroup$
                                          – tsh
                                          yesterday


















                                        • $begingroup$
                                          55 bytes
                                          $endgroup$
                                          – Embodiment of Ignorance
                                          yesterday












                                        • $begingroup$
                                          @EmbodimentofIgnorance I usually avoid that trick, as the eval'ed code is much slower. But the difference is barely noticeable for that one, so I guess that's fine.
                                          $endgroup$
                                          – Arnauld
                                          yesterday






                                        • 1




                                          $begingroup$
                                          But this is code-golf, we don't care about speed, as long as it gets the job done
                                          $endgroup$
                                          – Embodiment of Ignorance
                                          yesterday










                                        • $begingroup$
                                          n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")
                                          $endgroup$
                                          – tsh
                                          yesterday
















                                        $begingroup$
                                        55 bytes
                                        $endgroup$
                                        – Embodiment of Ignorance
                                        yesterday






                                        $begingroup$
                                        55 bytes
                                        $endgroup$
                                        – Embodiment of Ignorance
                                        yesterday














                                        $begingroup$
                                        @EmbodimentofIgnorance I usually avoid that trick, as the eval'ed code is much slower. But the difference is barely noticeable for that one, so I guess that's fine.
                                        $endgroup$
                                        – Arnauld
                                        yesterday




                                        $begingroup$
                                        @EmbodimentofIgnorance I usually avoid that trick, as the eval'ed code is much slower. But the difference is barely noticeable for that one, so I guess that's fine.
                                        $endgroup$
                                        – Arnauld
                                        yesterday




                                        1




                                        1




                                        $begingroup$
                                        But this is code-golf, we don't care about speed, as long as it gets the job done
                                        $endgroup$
                                        – Embodiment of Ignorance
                                        yesterday




                                        $begingroup$
                                        But this is code-golf, we don't care about speed, as long as it gets the job done
                                        $endgroup$
                                        – Embodiment of Ignorance
                                        yesterday












                                        $begingroup$
                                        n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")
                                        $endgroup$
                                        – tsh
                                        yesterday




                                        $begingroup$
                                        n=>eval("for(o=[p=2];n--;)o[p=o[q=p>>1]?3*p:q]=p")
                                        $endgroup$
                                        – tsh
                                        yesterday











                                        3












                                        $begingroup$


                                        Perl 6, 51 bytes





                                        {(1,3,{first *∉@_,@_[*-1]+>1,3*@_[*-1]}...*)[$_]}


                                        Try it online!



                                        Returns the 0-indexed element in the sequence. You can change this to 1-indexed by changing the starting elements to 0,1 instead of 1,3



                                        Explanation:



                                        {                                               }  # Anonymous code block
                                        ( ...*)[$_] # Index into the infinite sequence
                                        1,3 # That starts with 1,3
                                        ,{ } # And each element is
                                        first # The first of
                                        @_[*-1]+>1 # The previous element bitshifted one
                                        ,3*@_[*-1] # Triple the previous element
                                        *∉@_, # That hasn't appeared in the sequence





                                        share|improve this answer









                                        $endgroup$


















                                          3












                                          $begingroup$


                                          Perl 6, 51 bytes





                                          {(1,3,{first *∉@_,@_[*-1]+>1,3*@_[*-1]}...*)[$_]}


                                          Try it online!



                                          Returns the 0-indexed element in the sequence. You can change this to 1-indexed by changing the starting elements to 0,1 instead of 1,3



                                          Explanation:



                                          {                                               }  # Anonymous code block
                                          ( ...*)[$_] # Index into the infinite sequence
                                          1,3 # That starts with 1,3
                                          ,{ } # And each element is
                                          first # The first of
                                          @_[*-1]+>1 # The previous element bitshifted one
                                          ,3*@_[*-1] # Triple the previous element
                                          *∉@_, # That hasn't appeared in the sequence





                                          share|improve this answer









                                          $endgroup$
















                                            3












                                            3








                                            3





                                            $begingroup$


                                            Perl 6, 51 bytes





                                            {(1,3,{first *∉@_,@_[*-1]+>1,3*@_[*-1]}...*)[$_]}


                                            Try it online!



                                            Returns the 0-indexed element in the sequence. You can change this to 1-indexed by changing the starting elements to 0,1 instead of 1,3



                                            Explanation:



                                            {                                               }  # Anonymous code block
                                            ( ...*)[$_] # Index into the infinite sequence
                                            1,3 # That starts with 1,3
                                            ,{ } # And each element is
                                            first # The first of
                                            @_[*-1]+>1 # The previous element bitshifted one
                                            ,3*@_[*-1] # Triple the previous element
                                            *∉@_, # That hasn't appeared in the sequence





                                            share|improve this answer









                                            $endgroup$




                                            Perl 6, 51 bytes





                                            {(1,3,{first *∉@_,@_[*-1]+>1,3*@_[*-1]}...*)[$_]}


                                            Try it online!



                                            Returns the 0-indexed element in the sequence. You can change this to 1-indexed by changing the starting elements to 0,1 instead of 1,3



                                            Explanation:



                                            {                                               }  # Anonymous code block
                                            ( ...*)[$_] # Index into the infinite sequence
                                            1,3 # That starts with 1,3
                                            ,{ } # And each element is
                                            first # The first of
                                            @_[*-1]+>1 # The previous element bitshifted one
                                            ,3*@_[*-1] # Triple the previous element
                                            *∉@_, # That hasn't appeared in the sequence






                                            share|improve this answer












                                            share|improve this answer



                                            share|improve this answer










                                            answered yesterday









                                            Jo KingJo King

                                            26.6k364132




                                            26.6k364132























                                                3












                                                $begingroup$


                                                J, 47 40 bytes



                                                [:{:0 1(],<.@-:@{:@](e.{[,3*{:@])])^:[~]


                                                Try it online!



                                                ungolfed



                                                [: {: 0 1 (] , <.@-:@{:@] (e. { [ , 3 * {:@]) ])^:[~ ]


                                                Direct translation of the definition into J. It builds bottom up by using ^: to iterate from the starting value the required number of times.






                                                share|improve this answer











                                                $endgroup$


















                                                  3












                                                  $begingroup$


                                                  J, 47 40 bytes



                                                  [:{:0 1(],<.@-:@{:@](e.{[,3*{:@])])^:[~]


                                                  Try it online!



                                                  ungolfed



                                                  [: {: 0 1 (] , <.@-:@{:@] (e. { [ , 3 * {:@]) ])^:[~ ]


                                                  Direct translation of the definition into J. It builds bottom up by using ^: to iterate from the starting value the required number of times.






                                                  share|improve this answer











                                                  $endgroup$
















                                                    3












                                                    3








                                                    3





                                                    $begingroup$


                                                    J, 47 40 bytes



                                                    [:{:0 1(],<.@-:@{:@](e.{[,3*{:@])])^:[~]


                                                    Try it online!



                                                    ungolfed



                                                    [: {: 0 1 (] , <.@-:@{:@] (e. { [ , 3 * {:@]) ])^:[~ ]


                                                    Direct translation of the definition into J. It builds bottom up by using ^: to iterate from the starting value the required number of times.






                                                    share|improve this answer











                                                    $endgroup$




                                                    J, 47 40 bytes



                                                    [:{:0 1(],<.@-:@{:@](e.{[,3*{:@])])^:[~]


                                                    Try it online!



                                                    ungolfed



                                                    [: {: 0 1 (] , <.@-:@{:@] (e. { [ , 3 * {:@]) ])^:[~ ]


                                                    Direct translation of the definition into J. It builds bottom up by using ^: to iterate from the starting value the required number of times.







                                                    share|improve this answer














                                                    share|improve this answer



                                                    share|improve this answer








                                                    edited yesterday

























                                                    answered yesterday









                                                    JonahJonah

                                                    2,6611017




                                                    2,6611017























                                                        3












                                                        $begingroup$


                                                        05AB1E, 16 15 bytes



                                                        Saved 1 byte thanks to Kevin Cruijssen.

                                                        0-indexed.



                                                        ¾ˆ$FDˆx3*‚;ï¯Kн


                                                        Try it online!



                                                        Explanation



                                                        Using n=1 as example



                                                        ¾ˆ                 # initialize global array as [0]
                                                        $ # initialize stack with 1, input
                                                        F # input times do:
                                                        Dˆ # duplicate current item (initially 1) and add one copy to global array
                                                        # STACK: 1, GLOBAL_ARRAY: [0, 1]
                                                        x # push Top_of_stack*2
                                                        # STACK: 1, 2, GLOBAL_ARRAY: [0, 1]
                                                        3* # multiply by 3
                                                        # STACK: 1, 6, GLOBAL_ARRAY: [0, 1]
                                                        ‚;ï # pair and integer divide both by 2
                                                        # STACK: [0, 3], GLOBAL_ARRAY: [0, 1]
                                                        ¯K # remove any numbers already in the global array
                                                        # STACK: [3], GLOBAL_ARRAY: [0, 1]
                                                        н # and take the head
                                                        # STACK: 3





                                                        share|improve this answer











                                                        $endgroup$













                                                        • $begingroup$
                                                          15 bytes
                                                          $endgroup$
                                                          – Kevin Cruijssen
                                                          16 hours ago










                                                        • $begingroup$
                                                          @KevinCruijssen: Thanks! I thought of using the global array, but assumed it would be the same length as a list on the stack and never tried it :/
                                                          $endgroup$
                                                          – Emigna
                                                          16 hours ago
















                                                        3












                                                        $begingroup$


                                                        05AB1E, 16 15 bytes



                                                        Saved 1 byte thanks to Kevin Cruijssen.

                                                        0-indexed.



                                                        ¾ˆ$FDˆx3*‚;ï¯Kн


                                                        Try it online!



                                                        Explanation



                                                        Using n=1 as example



                                                        ¾ˆ                 # initialize global array as [0]
                                                        $ # initialize stack with 1, input
                                                        F # input times do:
                                                        Dˆ # duplicate current item (initially 1) and add one copy to global array
                                                        # STACK: 1, GLOBAL_ARRAY: [0, 1]
                                                        x # push Top_of_stack*2
                                                        # STACK: 1, 2, GLOBAL_ARRAY: [0, 1]
                                                        3* # multiply by 3
                                                        # STACK: 1, 6, GLOBAL_ARRAY: [0, 1]
                                                        ‚;ï # pair and integer divide both by 2
                                                        # STACK: [0, 3], GLOBAL_ARRAY: [0, 1]
                                                        ¯K # remove any numbers already in the global array
                                                        # STACK: [3], GLOBAL_ARRAY: [0, 1]
                                                        н # and take the head
                                                        # STACK: 3





                                                        share|improve this answer











                                                        $endgroup$













                                                        • $begingroup$
                                                          15 bytes
                                                          $endgroup$
                                                          – Kevin Cruijssen
                                                          16 hours ago










                                                        • $begingroup$
                                                          @KevinCruijssen: Thanks! I thought of using the global array, but assumed it would be the same length as a list on the stack and never tried it :/
                                                          $endgroup$
                                                          – Emigna
                                                          16 hours ago














                                                        3












                                                        3








                                                        3





                                                        $begingroup$


                                                        05AB1E, 16 15 bytes



                                                        Saved 1 byte thanks to Kevin Cruijssen.

                                                        0-indexed.



                                                        ¾ˆ$FDˆx3*‚;ï¯Kн


                                                        Try it online!



                                                        Explanation



                                                        Using n=1 as example



                                                        ¾ˆ                 # initialize global array as [0]
                                                        $ # initialize stack with 1, input
                                                        F # input times do:
                                                        Dˆ # duplicate current item (initially 1) and add one copy to global array
                                                        # STACK: 1, GLOBAL_ARRAY: [0, 1]
                                                        x # push Top_of_stack*2
                                                        # STACK: 1, 2, GLOBAL_ARRAY: [0, 1]
                                                        3* # multiply by 3
                                                        # STACK: 1, 6, GLOBAL_ARRAY: [0, 1]
                                                        ‚;ï # pair and integer divide both by 2
                                                        # STACK: [0, 3], GLOBAL_ARRAY: [0, 1]
                                                        ¯K # remove any numbers already in the global array
                                                        # STACK: [3], GLOBAL_ARRAY: [0, 1]
                                                        н # and take the head
                                                        # STACK: 3





                                                        share|improve this answer











                                                        $endgroup$




                                                        05AB1E, 16 15 bytes



                                                        Saved 1 byte thanks to Kevin Cruijssen.

                                                        0-indexed.



                                                        ¾ˆ$FDˆx3*‚;ï¯Kн


                                                        Try it online!



                                                        Explanation



                                                        Using n=1 as example



                                                        ¾ˆ                 # initialize global array as [0]
                                                        $ # initialize stack with 1, input
                                                        F # input times do:
                                                        Dˆ # duplicate current item (initially 1) and add one copy to global array
                                                        # STACK: 1, GLOBAL_ARRAY: [0, 1]
                                                        x # push Top_of_stack*2
                                                        # STACK: 1, 2, GLOBAL_ARRAY: [0, 1]
                                                        3* # multiply by 3
                                                        # STACK: 1, 6, GLOBAL_ARRAY: [0, 1]
                                                        ‚;ï # pair and integer divide both by 2
                                                        # STACK: [0, 3], GLOBAL_ARRAY: [0, 1]
                                                        ¯K # remove any numbers already in the global array
                                                        # STACK: [3], GLOBAL_ARRAY: [0, 1]
                                                        н # and take the head
                                                        # STACK: 3






                                                        share|improve this answer














                                                        share|improve this answer



                                                        share|improve this answer








                                                        edited 16 hours ago

























                                                        answered 22 hours ago









                                                        EmignaEmigna

                                                        47.6k433145




                                                        47.6k433145












                                                        • $begingroup$
                                                          15 bytes
                                                          $endgroup$
                                                          – Kevin Cruijssen
                                                          16 hours ago










                                                        • $begingroup$
                                                          @KevinCruijssen: Thanks! I thought of using the global array, but assumed it would be the same length as a list on the stack and never tried it :/
                                                          $endgroup$
                                                          – Emigna
                                                          16 hours ago


















                                                        • $begingroup$
                                                          15 bytes
                                                          $endgroup$
                                                          – Kevin Cruijssen
                                                          16 hours ago










                                                        • $begingroup$
                                                          @KevinCruijssen: Thanks! I thought of using the global array, but assumed it would be the same length as a list on the stack and never tried it :/
                                                          $endgroup$
                                                          – Emigna
                                                          16 hours ago
















                                                        $begingroup$
                                                        15 bytes
                                                        $endgroup$
                                                        – Kevin Cruijssen
                                                        16 hours ago




                                                        $begingroup$
                                                        15 bytes
                                                        $endgroup$
                                                        – Kevin Cruijssen
                                                        16 hours ago












                                                        $begingroup$
                                                        @KevinCruijssen: Thanks! I thought of using the global array, but assumed it would be the same length as a list on the stack and never tried it :/
                                                        $endgroup$
                                                        – Emigna
                                                        16 hours ago




                                                        $begingroup$
                                                        @KevinCruijssen: Thanks! I thought of using the global array, but assumed it would be the same length as a list on the stack and never tried it :/
                                                        $endgroup$
                                                        – Emigna
                                                        16 hours ago











                                                        2












                                                        $begingroup$


                                                        Jelly, 21 bytes



                                                        Ø.;0ị×3$:2$:2eɗ?Ɗ$⁸¡Ṫ


                                                        Try it online!



                                                        A monadic link that takes zero-indexed $n$ as the argument and returns $a(n)$.






                                                        share|improve this answer









                                                        $endgroup$


















                                                          2












                                                          $begingroup$


                                                          Jelly, 21 bytes



                                                          Ø.;0ị×3$:2$:2eɗ?Ɗ$⁸¡Ṫ


                                                          Try it online!



                                                          A monadic link that takes zero-indexed $n$ as the argument and returns $a(n)$.






                                                          share|improve this answer









                                                          $endgroup$
















                                                            2












                                                            2








                                                            2





                                                            $begingroup$


                                                            Jelly, 21 bytes



                                                            Ø.;0ị×3$:2$:2eɗ?Ɗ$⁸¡Ṫ


                                                            Try it online!



                                                            A monadic link that takes zero-indexed $n$ as the argument and returns $a(n)$.






                                                            share|improve this answer









                                                            $endgroup$




                                                            Jelly, 21 bytes



                                                            Ø.;0ị×3$:2$:2eɗ?Ɗ$⁸¡Ṫ


                                                            Try it online!



                                                            A monadic link that takes zero-indexed $n$ as the argument and returns $a(n)$.







                                                            share|improve this answer












                                                            share|improve this answer



                                                            share|improve this answer










                                                            answered yesterday









                                                            Nick KennedyNick Kennedy

                                                            1,36649




                                                            1,36649























                                                                2












                                                                $begingroup$

                                                                Java 10, 120 99 bytes





                                                                n->{var L=" 1 0 ";int r=1,t;for(;n-->0;L+=r+" ")if(L.contains(" "+(r=(t=r)/2)+" "))r=t*3;return r;}


                                                                Try it online.



                                                                Explanation:



                                                                n->{                              // Method with integer as both parameter and return-type
                                                                var L=" 1 0 "; // Create a String that acts as 'List', starting at [1,0]
                                                                int r=1, // Result-integer, starting at 1
                                                                t; // Temp-integer, uninitialized
                                                                for(;n-->0; // Loop the input amount of times:
                                                                L+=r+" ")) // After every iteration: add the result to the 'List'
                                                                t=r // Create a copy of the result in `t`
                                                                r=(...)/2 // Then integer-divide the result by 2
                                                                if(L.contains(" "+(...)+" ")) // If the 'List' contains this result//2:
                                                                r=t*3; // Set the result to `t` multiplied by 3 instead
                                                                return r;} // Return the result





                                                                share|improve this answer











                                                                $endgroup$


















                                                                  2












                                                                  $begingroup$

                                                                  Java 10, 120 99 bytes





                                                                  n->{var L=" 1 0 ";int r=1,t;for(;n-->0;L+=r+" ")if(L.contains(" "+(r=(t=r)/2)+" "))r=t*3;return r;}


                                                                  Try it online.



                                                                  Explanation:



                                                                  n->{                              // Method with integer as both parameter and return-type
                                                                  var L=" 1 0 "; // Create a String that acts as 'List', starting at [1,0]
                                                                  int r=1, // Result-integer, starting at 1
                                                                  t; // Temp-integer, uninitialized
                                                                  for(;n-->0; // Loop the input amount of times:
                                                                  L+=r+" ")) // After every iteration: add the result to the 'List'
                                                                  t=r // Create a copy of the result in `t`
                                                                  r=(...)/2 // Then integer-divide the result by 2
                                                                  if(L.contains(" "+(...)+" ")) // If the 'List' contains this result//2:
                                                                  r=t*3; // Set the result to `t` multiplied by 3 instead
                                                                  return r;} // Return the result





                                                                  share|improve this answer











                                                                  $endgroup$
















                                                                    2












                                                                    2








                                                                    2





                                                                    $begingroup$

                                                                    Java 10, 120 99 bytes





                                                                    n->{var L=" 1 0 ";int r=1,t;for(;n-->0;L+=r+" ")if(L.contains(" "+(r=(t=r)/2)+" "))r=t*3;return r;}


                                                                    Try it online.



                                                                    Explanation:



                                                                    n->{                              // Method with integer as both parameter and return-type
                                                                    var L=" 1 0 "; // Create a String that acts as 'List', starting at [1,0]
                                                                    int r=1, // Result-integer, starting at 1
                                                                    t; // Temp-integer, uninitialized
                                                                    for(;n-->0; // Loop the input amount of times:
                                                                    L+=r+" ")) // After every iteration: add the result to the 'List'
                                                                    t=r // Create a copy of the result in `t`
                                                                    r=(...)/2 // Then integer-divide the result by 2
                                                                    if(L.contains(" "+(...)+" ")) // If the 'List' contains this result//2:
                                                                    r=t*3; // Set the result to `t` multiplied by 3 instead
                                                                    return r;} // Return the result





                                                                    share|improve this answer











                                                                    $endgroup$



                                                                    Java 10, 120 99 bytes





                                                                    n->{var L=" 1 0 ";int r=1,t;for(;n-->0;L+=r+" ")if(L.contains(" "+(r=(t=r)/2)+" "))r=t*3;return r;}


                                                                    Try it online.



                                                                    Explanation:



                                                                    n->{                              // Method with integer as both parameter and return-type
                                                                    var L=" 1 0 "; // Create a String that acts as 'List', starting at [1,0]
                                                                    int r=1, // Result-integer, starting at 1
                                                                    t; // Temp-integer, uninitialized
                                                                    for(;n-->0; // Loop the input amount of times:
                                                                    L+=r+" ")) // After every iteration: add the result to the 'List'
                                                                    t=r // Create a copy of the result in `t`
                                                                    r=(...)/2 // Then integer-divide the result by 2
                                                                    if(L.contains(" "+(...)+" ")) // If the 'List' contains this result//2:
                                                                    r=t*3; // Set the result to `t` multiplied by 3 instead
                                                                    return r;} // Return the result






                                                                    share|improve this answer














                                                                    share|improve this answer



                                                                    share|improve this answer








                                                                    edited 16 hours ago

























                                                                    answered 16 hours ago









                                                                    Kevin CruijssenKevin Cruijssen

                                                                    42.4k570217




                                                                    42.4k570217























                                                                        2












                                                                        $begingroup$


                                                                        Japt, 15 14 bytes



                                                                        1-indexed.



                                                                        @[X*3Xz]kZ Ì}g


                                                                        Try it



                                                                        @[X*3Xz]kZ Ì}g     :Implicit input of integer U
                                                                        g :Starting with the array [0,1] do the following U times, pushing the result to the array each time
                                                                        @ : Pass the last element X in the array Z through the following function
                                                                        [ : Build an array containing
                                                                        X*3 : X multiplied by 3
                                                                        Xz : X floor divided by 2
                                                                        ] : Close array
                                                                        kZ : Remove all elements contained in Z
                                                                        Ì : Get the last element
                                                                        } : End function
                                                                        :Implicit output of the last element in the array





                                                                        share|improve this answer











                                                                        $endgroup$


















                                                                          2












                                                                          $begingroup$


                                                                          Japt, 15 14 bytes



                                                                          1-indexed.



                                                                          @[X*3Xz]kZ Ì}g


                                                                          Try it



                                                                          @[X*3Xz]kZ Ì}g     :Implicit input of integer U
                                                                          g :Starting with the array [0,1] do the following U times, pushing the result to the array each time
                                                                          @ : Pass the last element X in the array Z through the following function
                                                                          [ : Build an array containing
                                                                          X*3 : X multiplied by 3
                                                                          Xz : X floor divided by 2
                                                                          ] : Close array
                                                                          kZ : Remove all elements contained in Z
                                                                          Ì : Get the last element
                                                                          } : End function
                                                                          :Implicit output of the last element in the array





                                                                          share|improve this answer











                                                                          $endgroup$
















                                                                            2












                                                                            2








                                                                            2





                                                                            $begingroup$


                                                                            Japt, 15 14 bytes



                                                                            1-indexed.



                                                                            @[X*3Xz]kZ Ì}g


                                                                            Try it



                                                                            @[X*3Xz]kZ Ì}g     :Implicit input of integer U
                                                                            g :Starting with the array [0,1] do the following U times, pushing the result to the array each time
                                                                            @ : Pass the last element X in the array Z through the following function
                                                                            [ : Build an array containing
                                                                            X*3 : X multiplied by 3
                                                                            Xz : X floor divided by 2
                                                                            ] : Close array
                                                                            kZ : Remove all elements contained in Z
                                                                            Ì : Get the last element
                                                                            } : End function
                                                                            :Implicit output of the last element in the array





                                                                            share|improve this answer











                                                                            $endgroup$




                                                                            Japt, 15 14 bytes



                                                                            1-indexed.



                                                                            @[X*3Xz]kZ Ì}g


                                                                            Try it



                                                                            @[X*3Xz]kZ Ì}g     :Implicit input of integer U
                                                                            g :Starting with the array [0,1] do the following U times, pushing the result to the array each time
                                                                            @ : Pass the last element X in the array Z through the following function
                                                                            [ : Build an array containing
                                                                            X*3 : X multiplied by 3
                                                                            Xz : X floor divided by 2
                                                                            ] : Close array
                                                                            kZ : Remove all elements contained in Z
                                                                            Ì : Get the last element
                                                                            } : End function
                                                                            :Implicit output of the last element in the array






                                                                            share|improve this answer














                                                                            share|improve this answer



                                                                            share|improve this answer








                                                                            edited 13 hours ago

























                                                                            answered 14 hours ago









                                                                            ShaggyShaggy

                                                                            18.9k21768




                                                                            18.9k21768























                                                                                2












                                                                                $begingroup$


                                                                                Haskell, 67 65 bytes





                                                                                (h[1,0]!!)
                                                                                h l@(a:o)|elem(div a 2)o=a:h(3*a:l)|1>0=a:h(div a 2:l)


                                                                                Try it online!



                                                                                Uses 0-based indexing.



                                                                                EDIT: saved 2 bytes by using elem instead of notElem and switching conditions






                                                                                share|improve this answer











                                                                                $endgroup$


















                                                                                  2












                                                                                  $begingroup$


                                                                                  Haskell, 67 65 bytes





                                                                                  (h[1,0]!!)
                                                                                  h l@(a:o)|elem(div a 2)o=a:h(3*a:l)|1>0=a:h(div a 2:l)


                                                                                  Try it online!



                                                                                  Uses 0-based indexing.



                                                                                  EDIT: saved 2 bytes by using elem instead of notElem and switching conditions






                                                                                  share|improve this answer











                                                                                  $endgroup$
















                                                                                    2












                                                                                    2








                                                                                    2





                                                                                    $begingroup$


                                                                                    Haskell, 67 65 bytes





                                                                                    (h[1,0]!!)
                                                                                    h l@(a:o)|elem(div a 2)o=a:h(3*a:l)|1>0=a:h(div a 2:l)


                                                                                    Try it online!



                                                                                    Uses 0-based indexing.



                                                                                    EDIT: saved 2 bytes by using elem instead of notElem and switching conditions






                                                                                    share|improve this answer











                                                                                    $endgroup$




                                                                                    Haskell, 67 65 bytes





                                                                                    (h[1,0]!!)
                                                                                    h l@(a:o)|elem(div a 2)o=a:h(3*a:l)|1>0=a:h(div a 2:l)


                                                                                    Try it online!



                                                                                    Uses 0-based indexing.



                                                                                    EDIT: saved 2 bytes by using elem instead of notElem and switching conditions







                                                                                    share|improve this answer














                                                                                    share|improve this answer



                                                                                    share|improve this answer








                                                                                    edited 13 hours ago

























                                                                                    answered 22 hours ago









                                                                                    user1472751user1472751

                                                                                    1,25126




                                                                                    1,25126























                                                                                        2












                                                                                        $begingroup$


                                                                                        Python 2, 66 bytes





                                                                                        l=lambda n,p=1,s=[0]:p*(n<len(s))or l(n,3*p*(p/2in s)or p/2,[p]+s)


                                                                                        Try it online!



                                                                                        Uses zero-based indexing. The lambda does little more than recursively building up the sequence and returning as soon as the required index is reached.






                                                                                        share|improve this answer









                                                                                        $endgroup$


















                                                                                          2












                                                                                          $begingroup$


                                                                                          Python 2, 66 bytes





                                                                                          l=lambda n,p=1,s=[0]:p*(n<len(s))or l(n,3*p*(p/2in s)or p/2,[p]+s)


                                                                                          Try it online!



                                                                                          Uses zero-based indexing. The lambda does little more than recursively building up the sequence and returning as soon as the required index is reached.






                                                                                          share|improve this answer









                                                                                          $endgroup$
















                                                                                            2












                                                                                            2








                                                                                            2





                                                                                            $begingroup$


                                                                                            Python 2, 66 bytes





                                                                                            l=lambda n,p=1,s=[0]:p*(n<len(s))or l(n,3*p*(p/2in s)or p/2,[p]+s)


                                                                                            Try it online!



                                                                                            Uses zero-based indexing. The lambda does little more than recursively building up the sequence and returning as soon as the required index is reached.






                                                                                            share|improve this answer









                                                                                            $endgroup$




                                                                                            Python 2, 66 bytes





                                                                                            l=lambda n,p=1,s=[0]:p*(n<len(s))or l(n,3*p*(p/2in s)or p/2,[p]+s)


                                                                                            Try it online!



                                                                                            Uses zero-based indexing. The lambda does little more than recursively building up the sequence and returning as soon as the required index is reached.







                                                                                            share|improve this answer












                                                                                            share|improve this answer



                                                                                            share|improve this answer










                                                                                            answered 9 hours ago









                                                                                            ArBoArBo

                                                                                            38115




                                                                                            38115























                                                                                                1












                                                                                                $begingroup$


                                                                                                Wolfram Language (Mathematica), 63 bytes



                                                                                                (L=Last)@Nest[{##,If[FreeQ[#,x=⌊L@#/2⌋],x,3L@#]}&,{0,1},#]&


                                                                                                Try it online!



                                                                                                This is 0-indexed

                                                                                                (In TIO I added -1 in every test case)






                                                                                                share|improve this answer











                                                                                                $endgroup$


















                                                                                                  1












                                                                                                  $begingroup$


                                                                                                  Wolfram Language (Mathematica), 63 bytes



                                                                                                  (L=Last)@Nest[{##,If[FreeQ[#,x=⌊L@#/2⌋],x,3L@#]}&,{0,1},#]&


                                                                                                  Try it online!



                                                                                                  This is 0-indexed

                                                                                                  (In TIO I added -1 in every test case)






                                                                                                  share|improve this answer











                                                                                                  $endgroup$
















                                                                                                    1












                                                                                                    1








                                                                                                    1





                                                                                                    $begingroup$


                                                                                                    Wolfram Language (Mathematica), 63 bytes



                                                                                                    (L=Last)@Nest[{##,If[FreeQ[#,x=⌊L@#/2⌋],x,3L@#]}&,{0,1},#]&


                                                                                                    Try it online!



                                                                                                    This is 0-indexed

                                                                                                    (In TIO I added -1 in every test case)






                                                                                                    share|improve this answer











                                                                                                    $endgroup$




                                                                                                    Wolfram Language (Mathematica), 63 bytes



                                                                                                    (L=Last)@Nest[{##,If[FreeQ[#,x=⌊L@#/2⌋],x,3L@#]}&,{0,1},#]&


                                                                                                    Try it online!



                                                                                                    This is 0-indexed

                                                                                                    (In TIO I added -1 in every test case)







                                                                                                    share|improve this answer














                                                                                                    share|improve this answer



                                                                                                    share|improve this answer








                                                                                                    edited yesterday

























                                                                                                    answered yesterday









                                                                                                    J42161217J42161217

                                                                                                    13.9k21353




                                                                                                    13.9k21353























                                                                                                        1












                                                                                                        $begingroup$


                                                                                                        Ruby, 54 52 48 bytes





                                                                                                        ->n{*s=0;j=2;n.times{s<<j=s==s-[j/2]?j/2:j*3};j}


                                                                                                        Try it online!






                                                                                                        share|improve this answer











                                                                                                        $endgroup$


















                                                                                                          1












                                                                                                          $begingroup$


                                                                                                          Ruby, 54 52 48 bytes





                                                                                                          ->n{*s=0;j=2;n.times{s<<j=s==s-[j/2]?j/2:j*3};j}


                                                                                                          Try it online!






                                                                                                          share|improve this answer











                                                                                                          $endgroup$
















                                                                                                            1












                                                                                                            1








                                                                                                            1





                                                                                                            $begingroup$


                                                                                                            Ruby, 54 52 48 bytes





                                                                                                            ->n{*s=0;j=2;n.times{s<<j=s==s-[j/2]?j/2:j*3};j}


                                                                                                            Try it online!






                                                                                                            share|improve this answer











                                                                                                            $endgroup$




                                                                                                            Ruby, 54 52 48 bytes





                                                                                                            ->n{*s=0;j=2;n.times{s<<j=s==s-[j/2]?j/2:j*3};j}


                                                                                                            Try it online!







                                                                                                            share|improve this answer














                                                                                                            share|improve this answer



                                                                                                            share|improve this answer








                                                                                                            edited 16 hours ago

























                                                                                                            answered 17 hours ago









                                                                                                            Kirill L.Kirill L.

                                                                                                            6,0581527




                                                                                                            6,0581527























                                                                                                                1












                                                                                                                $begingroup$


                                                                                                                C++ (gcc), 189 180 bytes



                                                                                                                -9 bytes to small golfing





                                                                                                                #import<vector>
                                                                                                                #import<algorithm>
                                                                                                                int a(int n){std::vector<int>s={1};for(int i=0;i<n;++i)s.push_back(i&&std::find(s.begin(),s.end(),s[i]/2)==s.end()?s[i]/2:3*s[i]);return s[n-1];}


                                                                                                                Try it online!



                                                                                                                Computes the sequence up to n, then returns the desired element. Slow for larger indices.






                                                                                                                share|improve this answer











                                                                                                                $endgroup$


















                                                                                                                  1












                                                                                                                  $begingroup$


                                                                                                                  C++ (gcc), 189 180 bytes



                                                                                                                  -9 bytes to small golfing





                                                                                                                  #import<vector>
                                                                                                                  #import<algorithm>
                                                                                                                  int a(int n){std::vector<int>s={1};for(int i=0;i<n;++i)s.push_back(i&&std::find(s.begin(),s.end(),s[i]/2)==s.end()?s[i]/2:3*s[i]);return s[n-1];}


                                                                                                                  Try it online!



                                                                                                                  Computes the sequence up to n, then returns the desired element. Slow for larger indices.






                                                                                                                  share|improve this answer











                                                                                                                  $endgroup$
















                                                                                                                    1












                                                                                                                    1








                                                                                                                    1





                                                                                                                    $begingroup$


                                                                                                                    C++ (gcc), 189 180 bytes



                                                                                                                    -9 bytes to small golfing





                                                                                                                    #import<vector>
                                                                                                                    #import<algorithm>
                                                                                                                    int a(int n){std::vector<int>s={1};for(int i=0;i<n;++i)s.push_back(i&&std::find(s.begin(),s.end(),s[i]/2)==s.end()?s[i]/2:3*s[i]);return s[n-1];}


                                                                                                                    Try it online!



                                                                                                                    Computes the sequence up to n, then returns the desired element. Slow for larger indices.






                                                                                                                    share|improve this answer











                                                                                                                    $endgroup$




                                                                                                                    C++ (gcc), 189 180 bytes



                                                                                                                    -9 bytes to small golfing





                                                                                                                    #import<vector>
                                                                                                                    #import<algorithm>
                                                                                                                    int a(int n){std::vector<int>s={1};for(int i=0;i<n;++i)s.push_back(i&&std::find(s.begin(),s.end(),s[i]/2)==s.end()?s[i]/2:3*s[i]);return s[n-1];}


                                                                                                                    Try it online!



                                                                                                                    Computes the sequence up to n, then returns the desired element. Slow for larger indices.







                                                                                                                    share|improve this answer














                                                                                                                    share|improve this answer



                                                                                                                    share|improve this answer








                                                                                                                    edited 9 hours ago

























                                                                                                                    answered yesterday









                                                                                                                    Neil A.Neil A.

                                                                                                                    1,348120




                                                                                                                    1,348120























                                                                                                                        1












                                                                                                                        $begingroup$


                                                                                                                        Stax, 14 bytes



                                                                                                                        üÑα↕○Ü1∟¡f↑ô┬♥


                                                                                                                        Run and debug it



                                                                                                                        Zero-indexed.






                                                                                                                        share|improve this answer









                                                                                                                        $endgroup$


















                                                                                                                          1












                                                                                                                          $begingroup$


                                                                                                                          Stax, 14 bytes



                                                                                                                          üÑα↕○Ü1∟¡f↑ô┬♥


                                                                                                                          Run and debug it



                                                                                                                          Zero-indexed.






                                                                                                                          share|improve this answer









                                                                                                                          $endgroup$
















                                                                                                                            1












                                                                                                                            1








                                                                                                                            1





                                                                                                                            $begingroup$


                                                                                                                            Stax, 14 bytes



                                                                                                                            üÑα↕○Ü1∟¡f↑ô┬♥


                                                                                                                            Run and debug it



                                                                                                                            Zero-indexed.






                                                                                                                            share|improve this answer









                                                                                                                            $endgroup$




                                                                                                                            Stax, 14 bytes



                                                                                                                            üÑα↕○Ü1∟¡f↑ô┬♥


                                                                                                                            Run and debug it



                                                                                                                            Zero-indexed.







                                                                                                                            share|improve this answer












                                                                                                                            share|improve this answer



                                                                                                                            share|improve this answer










                                                                                                                            answered 8 hours ago









                                                                                                                            recursiverecursive

                                                                                                                            5,7291322




                                                                                                                            5,7291322























                                                                                                                                1












                                                                                                                                $begingroup$


                                                                                                                                Python 2, 62 bytes





                                                                                                                                a=lambda n:n<1or a(n-1)*6**(a(n-1)//2in[0]+map(a,range(n)))//2


                                                                                                                                Try it online!



                                                                                                                                Returns True for a(0). 0-indexed.






                                                                                                                                share|improve this answer









                                                                                                                                $endgroup$


















                                                                                                                                  1












                                                                                                                                  $begingroup$


                                                                                                                                  Python 2, 62 bytes





                                                                                                                                  a=lambda n:n<1or a(n-1)*6**(a(n-1)//2in[0]+map(a,range(n)))//2


                                                                                                                                  Try it online!



                                                                                                                                  Returns True for a(0). 0-indexed.






                                                                                                                                  share|improve this answer









                                                                                                                                  $endgroup$
















                                                                                                                                    1












                                                                                                                                    1








                                                                                                                                    1





                                                                                                                                    $begingroup$


                                                                                                                                    Python 2, 62 bytes





                                                                                                                                    a=lambda n:n<1or a(n-1)*6**(a(n-1)//2in[0]+map(a,range(n)))//2


                                                                                                                                    Try it online!



                                                                                                                                    Returns True for a(0). 0-indexed.






                                                                                                                                    share|improve this answer









                                                                                                                                    $endgroup$




                                                                                                                                    Python 2, 62 bytes





                                                                                                                                    a=lambda n:n<1or a(n-1)*6**(a(n-1)//2in[0]+map(a,range(n)))//2


                                                                                                                                    Try it online!



                                                                                                                                    Returns True for a(0). 0-indexed.







                                                                                                                                    share|improve this answer












                                                                                                                                    share|improve this answer



                                                                                                                                    share|improve this answer










                                                                                                                                    answered 7 hours ago









                                                                                                                                    Erik the OutgolferErik the Outgolfer

                                                                                                                                    33k429106




                                                                                                                                    33k429106























                                                                                                                                        1












                                                                                                                                        $begingroup$


                                                                                                                                        Python 3, 105 103 100 95 83 bytes



                                                                                                                                        -2 bytes thanks to agtoever
                                                                                                                                        -12 bytes thanks to ArBo





                                                                                                                                        def f(n):
                                                                                                                                        s=0,1
                                                                                                                                        while len(s)<=n:t=s[-1]//2;s+=(t in s)*3*s[-1]or t,
                                                                                                                                        return s[-1]


                                                                                                                                        Try it online!






                                                                                                                                        share|improve this answer











                                                                                                                                        $endgroup$













                                                                                                                                        • $begingroup$
                                                                                                                                          You can replace the for loop with while len(s)<=n and replace the i's with -1. This should shave off one of two characters.
                                                                                                                                          $endgroup$
                                                                                                                                          – agtoever
                                                                                                                                          17 hours ago










                                                                                                                                        • $begingroup$
                                                                                                                                          @agtoever that's so clever - thanks! :)
                                                                                                                                          $endgroup$
                                                                                                                                          – Noodle9
                                                                                                                                          15 hours ago










                                                                                                                                        • $begingroup$
                                                                                                                                          83 bytes by working with a tuple instead of a list, and removing the if from the while loop to allow one-lining that loop
                                                                                                                                          $endgroup$
                                                                                                                                          – ArBo
                                                                                                                                          9 hours ago












                                                                                                                                        • $begingroup$
                                                                                                                                          @ArBo wow! absolutely brilliant - thanks :)
                                                                                                                                          $endgroup$
                                                                                                                                          – Noodle9
                                                                                                                                          6 hours ago
















                                                                                                                                        1












                                                                                                                                        $begingroup$


                                                                                                                                        Python 3, 105 103 100 95 83 bytes



                                                                                                                                        -2 bytes thanks to agtoever
                                                                                                                                        -12 bytes thanks to ArBo





                                                                                                                                        def f(n):
                                                                                                                                        s=0,1
                                                                                                                                        while len(s)<=n:t=s[-1]//2;s+=(t in s)*3*s[-1]or t,
                                                                                                                                        return s[-1]


                                                                                                                                        Try it online!






                                                                                                                                        share|improve this answer











                                                                                                                                        $endgroup$













                                                                                                                                        • $begingroup$
                                                                                                                                          You can replace the for loop with while len(s)<=n and replace the i's with -1. This should shave off one of two characters.
                                                                                                                                          $endgroup$
                                                                                                                                          – agtoever
                                                                                                                                          17 hours ago










                                                                                                                                        • $begingroup$
                                                                                                                                          @agtoever that's so clever - thanks! :)
                                                                                                                                          $endgroup$
                                                                                                                                          – Noodle9
                                                                                                                                          15 hours ago










                                                                                                                                        • $begingroup$
                                                                                                                                          83 bytes by working with a tuple instead of a list, and removing the if from the while loop to allow one-lining that loop
                                                                                                                                          $endgroup$
                                                                                                                                          – ArBo
                                                                                                                                          9 hours ago












                                                                                                                                        • $begingroup$
                                                                                                                                          @ArBo wow! absolutely brilliant - thanks :)
                                                                                                                                          $endgroup$
                                                                                                                                          – Noodle9
                                                                                                                                          6 hours ago














                                                                                                                                        1












                                                                                                                                        1








                                                                                                                                        1





                                                                                                                                        $begingroup$


                                                                                                                                        Python 3, 105 103 100 95 83 bytes



                                                                                                                                        -2 bytes thanks to agtoever
                                                                                                                                        -12 bytes thanks to ArBo





                                                                                                                                        def f(n):
                                                                                                                                        s=0,1
                                                                                                                                        while len(s)<=n:t=s[-1]//2;s+=(t in s)*3*s[-1]or t,
                                                                                                                                        return s[-1]


                                                                                                                                        Try it online!






                                                                                                                                        share|improve this answer











                                                                                                                                        $endgroup$




                                                                                                                                        Python 3, 105 103 100 95 83 bytes



                                                                                                                                        -2 bytes thanks to agtoever
                                                                                                                                        -12 bytes thanks to ArBo





                                                                                                                                        def f(n):
                                                                                                                                        s=0,1
                                                                                                                                        while len(s)<=n:t=s[-1]//2;s+=(t in s)*3*s[-1]or t,
                                                                                                                                        return s[-1]


                                                                                                                                        Try it online!







                                                                                                                                        share|improve this answer














                                                                                                                                        share|improve this answer



                                                                                                                                        share|improve this answer








                                                                                                                                        edited 6 hours ago

























                                                                                                                                        answered 17 hours ago









                                                                                                                                        Noodle9Noodle9

                                                                                                                                        29137




                                                                                                                                        29137












                                                                                                                                        • $begingroup$
                                                                                                                                          You can replace the for loop with while len(s)<=n and replace the i's with -1. This should shave off one of two characters.
                                                                                                                                          $endgroup$
                                                                                                                                          – agtoever
                                                                                                                                          17 hours ago










                                                                                                                                        • $begingroup$
                                                                                                                                          @agtoever that's so clever - thanks! :)
                                                                                                                                          $endgroup$
                                                                                                                                          – Noodle9
                                                                                                                                          15 hours ago










                                                                                                                                        • $begingroup$
                                                                                                                                          83 bytes by working with a tuple instead of a list, and removing the if from the while loop to allow one-lining that loop
                                                                                                                                          $endgroup$
                                                                                                                                          – ArBo
                                                                                                                                          9 hours ago












                                                                                                                                        • $begingroup$
                                                                                                                                          @ArBo wow! absolutely brilliant - thanks :)
                                                                                                                                          $endgroup$
                                                                                                                                          – Noodle9
                                                                                                                                          6 hours ago


















                                                                                                                                        • $begingroup$
                                                                                                                                          You can replace the for loop with while len(s)<=n and replace the i's with -1. This should shave off one of two characters.
                                                                                                                                          $endgroup$
                                                                                                                                          – agtoever
                                                                                                                                          17 hours ago










                                                                                                                                        • $begingroup$
                                                                                                                                          @agtoever that's so clever - thanks! :)
                                                                                                                                          $endgroup$
                                                                                                                                          – Noodle9
                                                                                                                                          15 hours ago










                                                                                                                                        • $begingroup$
                                                                                                                                          83 bytes by working with a tuple instead of a list, and removing the if from the while loop to allow one-lining that loop
                                                                                                                                          $endgroup$
                                                                                                                                          – ArBo
                                                                                                                                          9 hours ago












                                                                                                                                        • $begingroup$
                                                                                                                                          @ArBo wow! absolutely brilliant - thanks :)
                                                                                                                                          $endgroup$
                                                                                                                                          – Noodle9
                                                                                                                                          6 hours ago
















                                                                                                                                        $begingroup$
                                                                                                                                        You can replace the for loop with while len(s)<=n and replace the i's with -1. This should shave off one of two characters.
                                                                                                                                        $endgroup$
                                                                                                                                        – agtoever
                                                                                                                                        17 hours ago




                                                                                                                                        $begingroup$
                                                                                                                                        You can replace the for loop with while len(s)<=n and replace the i's with -1. This should shave off one of two characters.
                                                                                                                                        $endgroup$
                                                                                                                                        – agtoever
                                                                                                                                        17 hours ago












                                                                                                                                        $begingroup$
                                                                                                                                        @agtoever that's so clever - thanks! :)
                                                                                                                                        $endgroup$
                                                                                                                                        – Noodle9
                                                                                                                                        15 hours ago




                                                                                                                                        $begingroup$
                                                                                                                                        @agtoever that's so clever - thanks! :)
                                                                                                                                        $endgroup$
                                                                                                                                        – Noodle9
                                                                                                                                        15 hours ago












                                                                                                                                        $begingroup$
                                                                                                                                        83 bytes by working with a tuple instead of a list, and removing the if from the while loop to allow one-lining that loop
                                                                                                                                        $endgroup$
                                                                                                                                        – ArBo
                                                                                                                                        9 hours ago






                                                                                                                                        $begingroup$
                                                                                                                                        83 bytes by working with a tuple instead of a list, and removing the if from the while loop to allow one-lining that loop
                                                                                                                                        $endgroup$
                                                                                                                                        – ArBo
                                                                                                                                        9 hours ago














                                                                                                                                        $begingroup$
                                                                                                                                        @ArBo wow! absolutely brilliant - thanks :)
                                                                                                                                        $endgroup$
                                                                                                                                        – Noodle9
                                                                                                                                        6 hours ago




                                                                                                                                        $begingroup$
                                                                                                                                        @ArBo wow! absolutely brilliant - thanks :)
                                                                                                                                        $endgroup$
                                                                                                                                        – Noodle9
                                                                                                                                        6 hours ago











                                                                                                                                        1












                                                                                                                                        $begingroup$


                                                                                                                                        Gaia, 22 20 bytes



                                                                                                                                        2…@⟨:):3פḥ⌋,;D)+⟩ₓ)


                                                                                                                                        Try it online!



                                                                                                                                        0-based index.



                                                                                                                                        Credit to Shaggy for the approach



                                                                                                                                        2…			| push [0 1]
                                                                                                                                        @⟨ ⟩ₓ | do the following n times:
                                                                                                                                        :): | dup the list L, take the last element e, and dup that
                                                                                                                                        3פḥ⌋, | push [3*e floor(e/2)]
                                                                                                                                        ;D | take the asymmetric set difference [3*e floor(e/2)] - L
                                                                                                                                        )+ | take the last element of the difference and add it to the end of L (end of loop)
                                                                                                                                        ) | finally, take the last element and output it


                                                                                                                                        ;D






                                                                                                                                        share|improve this answer











                                                                                                                                        $endgroup$


















                                                                                                                                          1












                                                                                                                                          $begingroup$


                                                                                                                                          Gaia, 22 20 bytes



                                                                                                                                          2…@⟨:):3פḥ⌋,;D)+⟩ₓ)


                                                                                                                                          Try it online!



                                                                                                                                          0-based index.



                                                                                                                                          Credit to Shaggy for the approach



                                                                                                                                          2…			| push [0 1]
                                                                                                                                          @⟨ ⟩ₓ | do the following n times:
                                                                                                                                          :): | dup the list L, take the last element e, and dup that
                                                                                                                                          3פḥ⌋, | push [3*e floor(e/2)]
                                                                                                                                          ;D | take the asymmetric set difference [3*e floor(e/2)] - L
                                                                                                                                          )+ | take the last element of the difference and add it to the end of L (end of loop)
                                                                                                                                          ) | finally, take the last element and output it


                                                                                                                                          ;D






                                                                                                                                          share|improve this answer











                                                                                                                                          $endgroup$
















                                                                                                                                            1












                                                                                                                                            1








                                                                                                                                            1





                                                                                                                                            $begingroup$


                                                                                                                                            Gaia, 22 20 bytes



                                                                                                                                            2…@⟨:):3פḥ⌋,;D)+⟩ₓ)


                                                                                                                                            Try it online!



                                                                                                                                            0-based index.



                                                                                                                                            Credit to Shaggy for the approach



                                                                                                                                            2…			| push [0 1]
                                                                                                                                            @⟨ ⟩ₓ | do the following n times:
                                                                                                                                            :): | dup the list L, take the last element e, and dup that
                                                                                                                                            3פḥ⌋, | push [3*e floor(e/2)]
                                                                                                                                            ;D | take the asymmetric set difference [3*e floor(e/2)] - L
                                                                                                                                            )+ | take the last element of the difference and add it to the end of L (end of loop)
                                                                                                                                            ) | finally, take the last element and output it


                                                                                                                                            ;D






                                                                                                                                            share|improve this answer











                                                                                                                                            $endgroup$




                                                                                                                                            Gaia, 22 20 bytes



                                                                                                                                            2…@⟨:):3פḥ⌋,;D)+⟩ₓ)


                                                                                                                                            Try it online!



                                                                                                                                            0-based index.



                                                                                                                                            Credit to Shaggy for the approach



                                                                                                                                            2…			| push [0 1]
                                                                                                                                            @⟨ ⟩ₓ | do the following n times:
                                                                                                                                            :): | dup the list L, take the last element e, and dup that
                                                                                                                                            3פḥ⌋, | push [3*e floor(e/2)]
                                                                                                                                            ;D | take the asymmetric set difference [3*e floor(e/2)] - L
                                                                                                                                            )+ | take the last element of the difference and add it to the end of L (end of loop)
                                                                                                                                            ) | finally, take the last element and output it


                                                                                                                                            ;D







                                                                                                                                            share|improve this answer














                                                                                                                                            share|improve this answer



                                                                                                                                            share|improve this answer








                                                                                                                                            edited 4 hours ago

























                                                                                                                                            answered 10 hours ago









                                                                                                                                            GiuseppeGiuseppe

                                                                                                                                            17.6k31153




                                                                                                                                            17.6k31153























                                                                                                                                                0












                                                                                                                                                $begingroup$


                                                                                                                                                Haskell, 55 bytes





                                                                                                                                                (1%[0]!!)
                                                                                                                                                a%o|b<-div a 2=a:last(b:[3*a|elem b o])%(a:o)


                                                                                                                                                Try it online!



                                                                                                                                                Golfing user1472751's slick list-generation method.



                                                                                                                                                Same length:





                                                                                                                                                (1%[0]!!)
                                                                                                                                                a%o=a:[x|x<-[div a 2,a*3],all(/=x)o]!!0%(a:o)


                                                                                                                                                Try it online!






                                                                                                                                                share|improve this answer











                                                                                                                                                $endgroup$


















                                                                                                                                                  0












                                                                                                                                                  $begingroup$


                                                                                                                                                  Haskell, 55 bytes





                                                                                                                                                  (1%[0]!!)
                                                                                                                                                  a%o|b<-div a 2=a:last(b:[3*a|elem b o])%(a:o)


                                                                                                                                                  Try it online!



                                                                                                                                                  Golfing user1472751's slick list-generation method.



                                                                                                                                                  Same length:





                                                                                                                                                  (1%[0]!!)
                                                                                                                                                  a%o=a:[x|x<-[div a 2,a*3],all(/=x)o]!!0%(a:o)


                                                                                                                                                  Try it online!






                                                                                                                                                  share|improve this answer











                                                                                                                                                  $endgroup$
















                                                                                                                                                    0












                                                                                                                                                    0








                                                                                                                                                    0





                                                                                                                                                    $begingroup$


                                                                                                                                                    Haskell, 55 bytes





                                                                                                                                                    (1%[0]!!)
                                                                                                                                                    a%o|b<-div a 2=a:last(b:[3*a|elem b o])%(a:o)


                                                                                                                                                    Try it online!



                                                                                                                                                    Golfing user1472751's slick list-generation method.



                                                                                                                                                    Same length:





                                                                                                                                                    (1%[0]!!)
                                                                                                                                                    a%o=a:[x|x<-[div a 2,a*3],all(/=x)o]!!0%(a:o)


                                                                                                                                                    Try it online!






                                                                                                                                                    share|improve this answer











                                                                                                                                                    $endgroup$




                                                                                                                                                    Haskell, 55 bytes





                                                                                                                                                    (1%[0]!!)
                                                                                                                                                    a%o|b<-div a 2=a:last(b:[3*a|elem b o])%(a:o)


                                                                                                                                                    Try it online!



                                                                                                                                                    Golfing user1472751's slick list-generation method.



                                                                                                                                                    Same length:





                                                                                                                                                    (1%[0]!!)
                                                                                                                                                    a%o=a:[x|x<-[div a 2,a*3],all(/=x)o]!!0%(a:o)


                                                                                                                                                    Try it online!







                                                                                                                                                    share|improve this answer














                                                                                                                                                    share|improve this answer



                                                                                                                                                    share|improve this answer








                                                                                                                                                    edited 17 hours ago

























                                                                                                                                                    answered 18 hours ago









                                                                                                                                                    xnorxnor

                                                                                                                                                    93.6k18190450




                                                                                                                                                    93.6k18190450






























                                                                                                                                                        draft saved

                                                                                                                                                        draft discarded




















































                                                                                                                                                        If this is an answer to a challenge…




                                                                                                                                                        • …Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.


                                                                                                                                                        • …Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one.
                                                                                                                                                          Explanations of your answer make it more interesting to read and are very much encouraged.


                                                                                                                                                        • …Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.



                                                                                                                                                        More generally…




                                                                                                                                                        • …Please make sure to answer the question and provide sufficient detail.


                                                                                                                                                        • …Avoid asking for help, clarification or responding to other answers (use comments instead).





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