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0-limiting word of the morphism 0->11, 1->001.
4

%I #41 Jul 27 2024 04:51:01

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

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

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

%N 0-limiting word of the morphism 0->11, 1->001.

%C The morphism 0->11, 1->001 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 11 -> 001001 -> 11110011111001 ->

%C 00100100100111110010010010010011111001; if the number of iterations is odd, the 1-word evolves from 0 -> 11 -> 001001 -> 11110011111001 , as in A285403.

%H Clark Kimberling, <a href="/A285177/b285177.txt">Table of n, a(n) for n = 1..10000</a>

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

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 0, 1}}] &, {0}, 10] (* A285177 *)

%t Flatten[Position[s, 0]] (* A285401 *)

%t Flatten[Position[s, 1]] (* A285402 *)

%Y Cf. A285401, A285402, A285403.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 26 2017