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%I #5 May 22 2017 20:03:22
%S 2,0,2,0,1,0,2,0,2,0,1,0,1,1,0,2,0,1,0,2,0,2,0,1,0,2,0,2,0,1,0,1,1,0,
%T 2,0,1,0,1,1,0,1,1,0,2,0,1,0,2,0,2,0,1,0,1,1,0,2,0,1,0,2,0,2,0,1,0,2,
%U 0,2,0,1,0,1,1,0,2,0,1,0,2,0,2,0,1,0
%N 0-limiting word of the morphism 0->10, 1->20, 2->1.
%C Starting with 0, the first 5 iterations of the morphism yield words shown here:
%C 1st: 10
%C 2nd: 2010
%C 3rd: 1102010
%C 4th: 2020101102010
%C 5th: 11011020102020101102010
%C The 0-limiting word is the limit of the words for which the number of iterations is even.
%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 = 2.246979603717467061050009768008...,
%C V = 2.801937735804838252472204639014...,
%C W = 5.048917339522305313522214407023...
%C 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 Clark Kimberling, <a href="/A287121/b287121.txt">Table of n, a(n) for n = 1..10000</a>
%e 2nd iterate: 2010
%e 4th iterate: 2020101102010
%e 6th iterate: 202010202010110201011011020102020101102010
%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 1}] &, {0}, 10] (* A287121 *)
%t Flatten[Position[s, 0]] (* A287122 *)
%t Flatten[Position[s, 1]] (* A287123 *)
%t Flatten[Position[s, 2]] (* A287124 *)
%Y Cf. A287122, A287123, A287124, A287129.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 22 2017
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