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Fixed point of the morphism 0 -> 01, 1 -> 1010.
3

%I #13 Oct 05 2020 09:36:39

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

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

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

%N Fixed point of the morphism 0 -> 01, 1 -> 1010.

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

%H Clark Kimberling, <a href="/A284912/b284912.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.

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

%e 0 -> 01-> 011010 -> 011010101001101001 ->

%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0, 1, 0}}] &, {0}, 6] (* A284912 *)

%t Flatten[Position[s, 0]] (* A284913 *)

%t Flatten[Position[s, 1]] (* A284914 *)

%Y Cf. A284913, A284914.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 17 2017