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

1,1

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

Table of n, a(n) for n=1..105.

Eric Angelini, Decimation-like sequences

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

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

Prog

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

Crossrefs

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

Sequence in context: A110161 A134667 A354354 * A285969 A189664 A260446

Adjacent sequences: A117940 A117941 A117942 * A117944 A117945 A117946

Keyword

nonn,easy

Author

Eric Angelini, May 03 2006

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

Status

approved