A285565 - OEIS

%I #4 Apr 30 2017 22:37:27

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

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

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

%N 0-limiting word of the morphism 0->11, 1-> 0110.

%C The morphism 0->11, 1-> 0110 has two limiting words.  If the number of iterations is even, the 0-word evolves from 0 -> 11 -> 01100110; if the number of iterations is odd, the 1-word evolves from 0 -> 11 -> 01100110 -> 110110011011110110011011, as in A285568.  See A285567 for a connection to the golden ratio.

%H Clark Kimberling, <a href="/A285565/b285565.txt">Table of n, a(n) for n = 1..10000</a>

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 1, 1, 0}}] &, {0}, 8] (* A285565 *)

%t Flatten[Position[s, 0]]  (* A285566 *)

%t Flatten[Position[s, 1]]  (* A285567 *)

%Y Cf. A285566, A285567, A285568, A285589.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 30 2017