%I
%S 1,0,0,1,1,0,1,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,1,
%T 0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,
%U 1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,1,0,1
%N 1limiting word of the morphism 0>10, 1> 011.
%C The morphism 0>10, 1>011 has two limiting words. If the number of iterations is even, the 0word evolves from 0 > 10 > 01110 > 1001101101110 > 0111010011011100110111001101101110, as in A285080; if the number of iterations is odd, the 1word evolves from 0 > 10 > 01110 > 1001101101110, as in A285083.
%C Let v(n) = position of nth 1. Then v(n)/n > (1+sqrt(5))/2, the golden ratio (A001622); see A285082.
%H Clark Kimberling, <a href="/A285083/b285083.txt">Table of n, a(n) for n = 1..10000</a>
%t s = Nest[Flatten[# /. {0 > {1, 0}, 1 > {0, 1, 1}}] &, {0}, 13]; (* A285083 *)
%t Flatten[Position[s, 0]]; (* A285084 *)
%t Flatten[Position[s, 1]]; (* A285085 *)
%Y Cf. A001622, A285080, A285084, A285085.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Apr 19 2017
