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Fixed point of the morphism 0 -> 01, 1 -> 0010.
3

%I #14 Nov 27 2023 23:21:54

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

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

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

%N Fixed point of the morphism 0 -> 01, 1 -> 0010.

%H Clark Kimberling, <a href="/A284772/b284772.txt">Table of n, a(n) for n = 1..10000</a>

%H Jeffrey Shallit, <a href="https://arxiv.org/abs/2310.14252">Proof of Irvine's conjecture via mechanized guessing</a>, arXiv preprint arXiv:2310.14252 [math.CO], revised version of November 24 2023.

%F a(n) = A286389(n-1) mod 2. - _Jeffrey Shallit_, Nov 27 2023

%e 0 -> 01-> 010010 -> 0100100101001001 -> ...

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

%t Flatten[Position[s, 0]] (* A284773 *)

%t Flatten[Position[s, 1]] (* A284774 *)

%Y Cf. A284773, A284774, A286389.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 13 2017