

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.


13



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
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OFFSET

1,1


COMMENTS

A selfgenerating sequence.
A superfractal? 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 A255824A255829 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, Decimationlike sequences
Eric Angelini, Decimationlike 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(nfloor(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: A109017 A110161 A134667 * 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



