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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.
12
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
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
Sequence in context: A110161 A134667 A354354 * A285969 A189664 A374413
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