|
%I #29 Sep 24 2018 16:53:14
%S 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,
%T 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,
%U 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
%N 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.
%C A self-generating sequence.
%C A super-fractal? Might also be called a lizard sequence (une suite du lézard) because it grows back from its tail.
%C Terms were computed by Gilles Sadowski.
%C First differences of Rauzy's sequence A071996. - _Benoit Cloitre_, Mar 10 2007
%C 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
%D J.-P. Delahaye, La suite du lézard et autres inventions, Pour la Science, No. 353, 2007.
%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Decimation.htm">Decimation-like sequences</a>
%H Eric Angelini, <a href="/A117943/a117943.pdf">Decimation-like sequences</a> [Cached copy, with permission]
%F 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
%o (PARI) a(n)=while(n>5,if(n%3,n-=n\3,n\=3));n==2 \\ _M. F. Hasler_, Mar 07 2015
%Y Cf. A178931, A255824, ..., A255829, A126616.
%K nonn,easy
%O 1,1
%A _Eric Angelini_, May 03 2006
%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jul 14 2007
%E Definition simplified by _M. F. Hasler_, Mar 07 2015
|
