A285252 - OEIS

%I #9 Oct 05 2020 10:55:47

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

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

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

%N 1-limiting word of the morphism 0->10, 1-> 0101.

%C The morphism 0->10, 1-> 0101 has two limiting words.  If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 0101 -> 100101100101 -> 010110100101100101010110100101100101; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 0101 -> 100101100101, as in A285252.

%C This is a 3-automatic sequence. See Allouche et al. link. - _Michel Dekking_, Oct 05 2020

%H Clark Kimberling, <a href="/A285252/b285252.txt">Table of n, a(n) for n = 1..10000</a>

%H J.-P. Allouche, F. M. Dekking, and M. Queffélec, <a href="https://arxiv.org/abs/2010.00920">Hidden automatic sequences</a>, arXiv:2010.00920 [math.NT], 2020.

%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 1, 0, 1}}] &, {0}, 11]; (* A285252 *)

%t Flatten[Position[s, 0]];  (* A285253 *)

%t Flatten[Position[s, 1]];  (* A285254 *)

%Y Cf. A285250, A285253, A285254.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 23 2017