A117943 a(1) = 0, a(2) = 1; a(3n) = a(n); if every third term (a(3), a(6), a(9), ...) is deleted, this gives back the original sequence.

0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1

Offset: 1

Author

Eric Angelini, May 03 2006

Keywords

• nonn
• easy

Comments

A self-generating sequence.

A super-fractal? Might also be called a lizard sequence (une suite du lézard) because it grows back from its tail.

Terms were computed by Gilles Sadowski.

First differences of Rauzy's sequence A071996. - Benoit Cloitre, Mar 10 2007

This is the characteristic sequence of A178931. Instead of "a(1)=0, a(2)=1", one could also say "Lexicographically earliest nontrivial sequence such that...". Starting with "a(1)=1, a(2)=2" would yield the m=3 analog of (the m=10 variant) A126616. See A255824-A255829 for the m=4,...,m=9 variants. - M. F. Hasler, Mar 07 2015

References

• J.-P. Delahaye, La suite du lézard et autres inventions, Pour la Science, No. 353, 2007.

Links

• Eric Angelini, Decimation-like sequences
• Eric Angelini, Decimation-like sequences [Cached copy, with permission]

Crossrefs

Cf. A178931, A255824, ..., A255829, A126616.

Programs

PARI

a(n)=while(n>5,if(n%3,n-=n\3,n\=3));n==2 \\ M. F. Hasler, Mar 07 2015

Formula

a(1)=0, a(1)=1; and for n>2, a(n)=a(n/3) if Mod(n,3)=0, a(n)=a(n-floor(n/3)) if Mod(n,3)>0. - John W. Layman, Feb 14 2007

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jul 14 2007

Definition simplified by M. F. Hasler, Mar 07 2015