A285159 - OEIS

%I #10 Oct 05 2020 10:55:32

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

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

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

%N 0-limiting word of the morphism 0->10, 1-> 0011.

%C The morphism 0->10, 1-> 0011 has two limiting words.  If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 001110 -> 101000110011001110 -> 001110001110101000110011101000110011101000110011001110; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 001110 -> 101000110011001110, as in A285162.

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

%H Clark Kimberling, <a href="/A285159/b285159.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, 0, 1, 1}}] &, {0}, 10]; (* A285159 *)

%t Flatten[Position[s, 0]];  (* A285160 *)

%t Flatten[Position[s, 1]];  (* A285161 *)

%Y Cf. A285160, A285161, A285162.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 21 2017