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A287179 1-limiting word of the morphism 0->10, 1->20, 2->1.

%I A287179 #5 May 23 2017 14:31:38
%S A287179 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 A287179 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 A287179 2,0,1,0,2,0,2,0,1,0,1,1,0,2,0,1,0,1
%N A287179 1-limiting word of the morphism 0->10, 1->20, 2->1.
%C A287179 Starting with 0, the first 5 iterations of the morphism yield words shown here:
%C A287179 1st:  10
%C A287179 2nd:  2010
%C A287179 3rd:  1102010
%C A287179 4th:  2020101102010
%C A287179 5th:  11011020102020101102010
%C A287179 The 1-limiting word is the limit of the words for which the number of iterations is odd.
%C A287179 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 A287179 U = 2.246979603717467061050009768008...,
%C A287179 V = 2.801937735804838252472204639014...,
%C A287179 W = 5.048917339522305313522214407023...
%C A287179 If n >=2, then u(n) - u(n-1) is in {2,3}, v(n) - v(n-1) is in {1,2,4,6}, and w(n) - w(n-1) is in {2,4,7,10}.
%H A287179 Clark Kimberling, <a href="/A287179/b287179.txt">Table of n, a(n) for n = 1..10000</a>
%e A287179 1st iterate: 10
%e A287179 3rd iterate: 1102010
%e A287179 5th iterate: 110110201020201011020100
%t A287179 s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 1}] &, {0}, 9] (* A287179 *)
%t A287179 Flatten[Position[s, 0]] (* A287180 *)
%t A287179 Flatten[Position[s, 1]] (* A287181 *)
%t A287179 Flatten[Position[s, 2]] (* A287182 *)
%Y A287179 Cf. A287121, A287180, A287181, A287182.
%K A287179 nonn,easy
%O A287179 1,7
%A A287179 _Clark Kimberling_, May 22 2017