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%I #5 May 21 2017 14:35:16
%S 0,1,2,2,0,0,0,1,0,1,0,1,2,2,0,1,2,2,0,1,2,2,0,0,0,1,2,2,0,0,0,1,2,2,
%T 0,0,0,1,0,1,0,1,2,2,0,0,0,1,0,1,0,1,2,2,0,0,0,1,0,1,0,1,2,2,0,1,2,2,
%U 0,1,2,2,0,0,0,1,0,1,0,1,2,2,0,1,2,2
%N Start with 0 and repeatedly substitute 0->01, 1->22, 2->0.
%C The fixed point of the morphism 0->01, 1->20, 2->1. Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2. 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 = 2.28537528186132044169516884721360670506...,
%C V = 3.87512979416277882597397059430967806752...,
%C W = 3.28537528186132044169516884721360670506...
%C If n >=2, then u(n) - u(n-1) is in {1,2,4}, v(n) - v(n-1) is in {2,4,6}, and w(n) - w(n-1) is in {1,3,5,9}.
%H Clark Kimberling, <a href="/A287086/b287086.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 10] (* A287086 *)
%t Flatten[Position[s, 0]] (* A287087 *)
%t Flatten[Position[s, 1]] (* A287088 *)
%t Flatten[Position[s, 2]] (* A287089 *)
%Y Cf. A287087, A287088, A287089.
%K nonn,easy
%O 1,3
%A _Clark Kimberling_, May 21 2017
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