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A126792 Removing the first, fourth, seventh, tenth ... term of the sequence yields the original sequence, augmented by 1.

%I A126792 #5 Sep 27 2013 09:19:48
%S A126792 0,1,2,1,3,2,2,4,3,1,3,5,3,4,2,2,4,6,2,4,5,4,3,3,3,5,7,1,3,5,3,6,5,5,
%T A126792 4,4,3,4,6,4,8,2,2,4,6,2,4,7,4,6,6,6,5,5,2,4,5,4,7,5,5,9,3,4,3,5,3,7,
%U A126792 3,3,5,8,3,5,7,5,7,7,7,6,6,1,3,5,3,6,5,5,8,6,3,6,10,6,4,5,5,4,6,5,4,8,4,4,4
%N A126792 Removing the first, fourth, seventh, tenth ... term of the sequence yields the original sequence, augmented by 1.
%C A126792 Inspired by the "decimation-like sequences" (or "suites du lezard", after Delahaye) of Eric Angelini.
%C A126792 This sequence is a generalization of sequence A000120, which is defined recursively by a(0)=0, a(2n)=a(n) and a(2n+1)=1+a(n). Its subsequence of even term is thus the original sequence while its subsequence of odd terms yields the original sequence augmented by 1.
%D A126792 Article by J-P. Delahaye in Pour la Science, mars 2007.
%e A126792 Removing parenthesised terms
%e A126792 (0),1,2,(1),3,2,(2),4,3,(1),3,5,(3),4,..
%e A126792 leaves
%e A126792 1,2, 3,2, 4,3, 3,5, 4,..
%e A126792 which is the original sequence with 1 added to each term.
%p A126792 liz:=n->if n=0 then 0 elif modp(n,3)=0 then liz(n/3) else 1+liz(n-1-floor(n/3)) fi;
%t A126792 a[0] = 0; a[n_] := a[n] = If[Mod[n, 3] == 0, a[n/3], a[Floor[(2*n - 1)/3]] + 1]; Table[a[n], {n, 0, 104}] (* _Jean-François Alcover_, Sep 27 2013 *)
%Y A126792 Cf. A117943.
%K A126792 nonn
%O A126792 0,3
%A A126792 _Roland Bacher_, Feb 20 2007, Feb 26 2007