%I
%S 1,1,0,1,1,0,2,0,1,0,1,1,0,1,1,0,2,0,1,0,2,0,2,0,1,0,1,1,0,2,0,1,0,1,
%T 1,0,1,1,0,2,0,1,0,1,1,0,1,1,0,2,0,1,0,2,0,2,0,1,0,1,1,0,2,0,1,0,2,0,
%U 2,0,1,0,2,0,2,0,1,0,1,1,0,2,0,1,0,1
%N 1limiting word of the morphism 0>10, 1>20, 2>1.
%C Starting with 0, the first 5 iterations of the morphism yield words shown here:
%C 1st: 10
%C 2nd: 2010
%C 3rd: 1102010
%C 4th: 2020101102010
%C 5th: 11011020102020101102010
%C The 1limiting word is the limit of the words for which the number of iterations is odd.
%C Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively. Then 1/U + 1/V + 1/W = 1, where
%C U = 2.246979603717467061050009768008...,
%C V = 2.801937735804838252472204639014...,
%C W = 5.048917339522305313522214407023...
%C If n >=2, then u(n)  u(n1) is in {2,3}, v(n)  v(n1) is in {1,2,4,6}, and w(n)  w(n1) is in {2,4,7,10}.
%H Clark Kimberling, <a href="/A287179/b287179.txt">Table of n, a(n) for n = 1..10000</a>
%e 1st iterate: 10
%e 3rd iterate: 1102010
%e 5th iterate: 110110201020201011020100
%t s = Nest[Flatten[# /. {0 > {1, 0}, 1 > {2, 0}, 2 > 1}] &, {0}, 9] (* A287179 *)
%t Flatten[Position[s, 0]] (* A287180 *)
%t Flatten[Position[s, 1]] (* A287181 *)
%t Flatten[Position[s, 2]] (* A287182 *)
%Y Cf. A287121, A287180, A287181, A287182.
%K nonn,easy
%O 1,7
%A _Clark Kimberling_, May 22 2017
