login
Image of 0 under repeated application of the morphism 0 -> 0,1,0, 1 -> 1,1,1.
26

%I #18 Sep 27 2019 19:44:50

%S 0,1,0,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,1,1,

%U 1,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N Image of 0 under repeated application of the morphism 0 -> 0,1,0, 1 -> 1,1,1.

%C A word that is pure uniform morphic and recurrent, but not primitive morphic.

%H Antti Karttunen, <a href="/A316829/b316829.txt">Table of n, a(n) for n = 0..19682</a>

%H Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, <a href="https://arxiv.org/abs/1711.10807">A Taxonomy of Morphic Sequences</a>, arXiv preprint arXiv:1711.10807 [cs.FL], Nov 29 2017.

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%F a(n) = 1 - A088917(n) = A105220(n) - 1. - _Antti Karttunen_, Sep 27 2019

%t SubstitutionSystem[{0 -> {0, 1, 0}, 1 -> {1, 1, 1}}, {0}, 5] // Last (* _Jean-François Alcover_, Aug 05 2018 *)

%o (PARI) A316829(n) = { while(n, if(n%3==1, return(1), n\=3)); (0); }; \\ _Antti Karttunen_, Sep 27 2019

%Y Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.

%Y Cf. A088917, A105220.

%Y Characteristic function of A081606.

%K nonn

%O 0

%A _N. J. A. Sloane_, Jul 15 2018