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%I #5 May 24 2017 17:25:49
%S 1,1,2,0,2,0,1,1,2,0,2,0,2,0,2,0,0,1,1,0,1,1,2,0,2,0,0,1,1,0,1,1,1,1,
%T 2,0,2,0,1,1,2,0,2,0,2,0,2,0,0,1,1,0,1,1,2,0,2,0,0,1,1,0,1,1,2,0,2,0,
%U 0,1,1,0,1,1,2,0,2,0,0,1,1,0,1,1,0,1
%N 1-limiting word of the morphism 0->11, 1->20, 2->0.
%C Starting with 0, the first 5 iterations of the morphism yield words shown here:
%C 1st: 11
%C 2nd: 2020
%C 3rd: 011011
%C 4th: 112020112020
%C 5th: 20200110112020011011
%C The 1-limiting word is the limit of the words for which the number of iterations congruent to 1 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 = 2.7692923542386314152404094643350334926...,
%C V = 2.4498438945029551040577327454145475624...,
%C W = 4.3344900716222708116779374775820643087...
%C If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,5,6,10}, and w(n) - w(n-1) is in {2,4,8,10,16}.
%H Clark Kimberling, <a href="/A287341/b287341.txt">Table of n, a(n) for n = 1..10000</a>
%e 3rd iterate: 011011
%e 6th iterate: 011011112020112020011011112020112020
%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {2, 0}, 2 -> 0}] &, {0}, 10] (* A287341 *)
%t Flatten[Position[s, 0]] (* A287342 *)
%t Flatten[Position[s, 1]] (* A287343 *)
%t Flatten[Position[s, 2]] (* A287344 *)
%Y Cf. A287337 (0-limiting word), A287342, A287343, A287344, A287345 (2-limiting word).
%K nonn,easy
%O 1,3
%A _Clark Kimberling_, May 24 2017
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