A285255 - OEIS

%I #10 Oct 05 2020 09:09:24

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

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

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

%N 0-limiting word of the morphism 0->10, 1-> 0110.

%C The morphism 0->10, 1-> 0110 has two limiting words.  If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 011010 -> 100110011010011010 -> 011010100110011010100110011010011010100110011010011010; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 011010 -> 100110011010011010, as in A285258.

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

%H Clark Kimberling, <a href="/A285255/b285255.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, 1, 0}}] &, {0}, 12]; (* A285255 *)

%t Flatten[Position[s, 0]];  (* A285256 *)

%t Flatten[Position[s, 1]];  (* A285257 *)

%Y Cf. A285256, A285257, A285258.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 23 2017