login
1-limiting word of the morphism 0->1, 1->0001.
4

%I #7 Apr 06 2017 21:46:12

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

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

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

%N 1-limiting word of the morphism 0->1, 1->0001.

%C The morphism 0->1, 1->0001 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 1 -> 0001 -> 1110001 -> 0001000100011110001; if the number of iterations is odd, the 1-word evolves from 0 -> 1 -> 0001 -> 1110001 ->, as in A284509.

%H Clark Kimberling, <a href="/A284512/b284512.txt">Table of n, a(n) for n = 1..10000</a>

%t s = Nest[Flatten[# /. {0 -> {1}, 1 -> {0, 0, 0, 1}}] &, {0}, 9] (* A284512 *)

%t Flatten[Position[s, 0]] (* A284513 *)

%t Flatten[Position[s, 1]] (* A284514 *)

%Y Cf. A284509, A284513, A284514.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 05 2017