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

0,3

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.

References

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

Links

Table of n, a(n) for n=0..104.

Example

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.

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 *)

Crossrefs

Cf. A117943.

Sequence in context: A086415 A069013 A029281 * A097367 A130211 A317207

Adjacent sequences: A126789 A126790 A126791 * A126793 A126794 A126795

Keyword

nonn

Author

Roland Bacher, Feb 20 2007, Feb 26 2007

Status

approved