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

%I A263390 #35 Jul 09 2021 17:43:35
%S A263390 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,
%T A263390 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,
%U A263390 20,0,9,21,14,6,22,4,15,23,10,1,24,16,7,25
%N A263390 a(3n) = n, otherwise a(n) = a(floor(2n/3)).
%C A263390 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.
%C A263390 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.
%C A263390 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.
%H A263390 Michael De Vlieger, <a href="/A263390/b263390.txt">Table of n, a(n) for n = 0..10000</a>
%F A263390 a(n) = A163491(n+1) - 1. - _Peter Munn_, Nov 22 2020
%t A263390 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 *)
%o A263390 (PARI) a(n)=if(n%3,a(2*n\3),n/3) \\ _Charles R Greathouse IV_, Apr 30 2016
%Y A263390 Comparable sequences: A025480, A163491.
%Y A263390 Ordinal transform: A087088.
%K A263390 nonn,easy
%O A263390 0,7
%A A263390 _Lee A. Newberg_, Apr 27 2016