%I
%S 0,1,0,2,0,1,0,1,0,2,0,1,0,0,1,0,2,0,1,0,2,0,1,0,0,1,0,2,0,1,0,1,0,2,
%T 0,1,0,0,1,0,2,0,1,0,1,0,2,0,1,0,0,1,0,2,0,1,0,2,0,1,0,0,1,0,2,0,1,0,
%U 1,0,2,0,1,0,0,1,0,2,0,1,0,0,1,0,2,0
%N 0limiting word of the morphism 0>10, 1>20, 2>0.
%C Starting with 0, the first 5 iterations of the morphism yield words shown here:
%C 1st: 10
%C 2nd: 2010
%C 3rd: 0102010
%C 4th: 1020100102010
%C 5th: 201001020101020100102010
%C The 2limiting word is the limit of the words for which the number of iterations is congruent to 2 mod 3.
%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 = 1.8392867552141611325518525646532866...,
%C V = U^2 = 3.3829757679062374941227085364...,
%C W = U^3 = 6.2222625231203986266745611011....
%C If n >=2, then u(n)  u(n1) is in {1,2}, v(n)  v(n1) is in {2,3,4}, and w(n)  w(n1) is in {4,6,7}.
%H Clark Kimberling, <a href="/A286998/b286998.txt">Table of n, a(n) for n = 1..10000</a>
%e 3rd iterate: 0102010
%e 6th iterate: 01020101020100102010201001020101020100102010
%t s = Nest[Flatten[# /. {0 > {1, 0}, 1 > {2, 0}, 2 > 0}] &, {0}, 9] (* A286998 *)
%t Flatten[Position[s, 0]] (* A286999 *)
%t Flatten[Position[s, 1]] (* A287000 *)
%t Flatten[Position[s, 2]] (* A287001 *)
%Y Cf. A286999, A287000, A287001, A287112, A287174.
%K nonn,easy
%O 1,4
%A _Clark Kimberling_, May 22 2017
