A263390 a(3n) = n, otherwise a(n) = a(floor(2n/3)).

0, 0, 0, 1, 0, 1, 2, 0, 1, 3, 2, 0, 4, 1, 3, 5, 2, 0, 6, 4, 1, 7, 3, 5, 8, 2, 0, 9, 6, 4, 10, 1, 7, 11, 3, 5, 12, 8, 2, 13, 0, 9, 14, 6, 4, 15, 10, 1, 16, 7, 11, 17, 3, 5, 18, 12, 8, 19, 2, 13, 20, 0, 9, 21, 14, 6, 22, 4, 15, 23, 10, 1, 24, 16, 7, 25

Offset: 0

Author

Lee A. Newberg, Apr 27 2016

Keywords

• nonn
• easy

Comments

This sequence is the unique fixed point of the function (a(0), a(1), a(2), ...) |--> (0, a(0), a(1), 1, a(2), a(3), 2, a(4), a(5), ...) which interleaves the nonnegative integers with pairs of elements of a sequence.

Compare with A025480, the unique fixed point of the function (a(0), a(1), a(2), ...) |--> (0, a(0), 1, a(1), 2, a(2), ...) which interleaves the nonnegative integers between the elements of a sequence.

These are the nim-values for heaps of n beans in the game where you're allowed to take up to one-third of the beans in a heap.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

Comparable sequences: A025480, A163491.

Ordinal transform: A087088.

Programs

Mathematica

Nest[Append[#1, If[Mod[#2, 3] == 0, #2/3, #1[[Floor[2 #2/3] + 1]]]] & @@ {#, Length[#]} &, {0}, 75] (* Michael De Vlieger, Jul 09 2021 *)

PARI

a(n)=if(n%3,a(2*n\3),n/3) \\ Charles R Greathouse IV, Apr 30 2016

Formula

a(n) = A163491(n+1) - 1. - Peter Munn, Nov 22 2020