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A287174 2-limiting word of the morphism 0->10, 1->20, 2->0.

%I A287174 #5 May 22 2017 20:03:33
%S A287174 2,0,1,0,0,1,0,2,0,1,0,1,0,2,0,1,0,0,1,0,2,0,1,0,0,1,0,2,0,1,0,1,0,2,
%T A287174 0,1,0,0,1,0,2,0,1,0,2,0,1,0,0,1,0,2,0,1,0,1,0,2,0,1,0,0,1,0,2,0,1,0,
%U A287174 1,0,2,0,1,0,0,1,0,2,0,1,0,2,0,1,0,0
%N A287174 2-limiting word of the morphism 0->10, 1->20, 2->0.
%C A287174 Starting with 0, the first 5 iterations of the morphism yield words shown here:
%C A287174 1st:  10
%C A287174 2nd:  2010
%C A287174 3rd:  0102010
%C A287174 4th:  1020100102010
%C A287174 5th:  201001020101020100102010
%C A287174 The 2-limiting word is the limit of the words for which the number of iterations is congruent to 2 mod 3.
%C A287174 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 A287174 U = 1.8392867552141611325518525646532866...,
%C A287174 V = U^2 = 3.3829757679062374941227085364...,
%C A287174 W = U^3 = 6.2222625231203986266745611011....
%C A287174 If n >=2, then u(n) - u(n-1) is in {1,2}, v(n) - v(n-1) is in {2,3,4}, and w(n) - w(n-1) is in {4,6,7}.
%H A287174 Clark Kimberling, <a href="/A287174/b287174.txt">Table of n, a(n) for n = 1..10000</a>
%e A287174 2nd iterate: 2010
%e A287174 5th iterate: 201001020101020100102010
%t A287174 s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 0}] &, {0}, 11] (* A287174 *)
%t A287174 Flatten[Position[s, 0]] (* A287175 *)
%t A287174 Flatten[Position[s, 1]] (* A287176 *)
%t A287174 Flatten[Position[s, 2]] (* A287177 *)
%Y A287174 Cf. A286998, A287111, A287175, A287176, A287177.
%K A287174 nonn,easy
%O A287174 1,1
%A A287174 _Clark Kimberling_, May 22 2017