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

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, 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, 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

Offset: 0

Author

Roland Bacher, Feb 20 2007, Feb 26 2007

Keywords

• nonn

Comments

Inspired by the "decimation-like sequences" (or "suites du lezard", after Delahaye) of Eric Angelini.

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.

Examples

			Removing parenthesised terms
(0),1,2,(1),3,2,(2),4,3,(1),3,5,(3),4,..
leaves
1,2, 3,2, 4,3, 3,5, 4,..
which is the original sequence with 1 added to each term.
		

References

• Article by J-P. Delahaye in Pour la Science, mars 2007.

Crossrefs

Cf. A117943.

Programs

Maple

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;

Mathematica

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 *)