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%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
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