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A287331 1-limiting word of the morphism 0->10, 1->22, 2->0, starting with 0.

%I A287331 #9 May 27 2021 17:17:36
%S A287331 1,0,1,0,0,0,2,2,1,0,1,0,1,0,0,0,2,2,1,0,0,0,2,2,1,0,0,0,2,2,1,0,2,2,
%T A287331 1,0,2,2,1,0,1,0,1,0,0,0,2,2,1,0,1,0,1,0,0,0,2,2,1,0,1,0,1,0,0,0,2,2,
%U A287331 1,0,0,0,2,2,1,0,0,0,2,2,1,0,2,2,1,0
%N A287331 1-limiting word of the morphism 0->10, 1->22, 2->0, starting with 0.
%C A287331 Starting with 0, the first 5 iterations of the morphism yield words shown here:
%C A287331 1st:  10
%C A287331 2nd:  2210
%C A287331 3rd:  002210
%C A287331 4th:  1010002210
%C A287331 5th:  221022101010002210
%C A287331 The 1-limiting word is the limit of the words for which the number of iterations is congruent to 1 mod 3.
%C A287331 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 A287331 U = 2.28537528186132044169516884721360670506...,
%C A287331 V = 3.87512979416277882597397059430967806752...,
%C A287331 W = 3.28537528186132044169516884721360670506...
%C A287331 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 A287331 Clark Kimberling, <a href="/A287331/b287331.txt">Table of n, a(n) for n = 1..10000</a>
%e A287331 1st iterate: 10
%e A287331 4th iterate: 1010002210
%t A287331 s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 10] (* A287331 *)
%t A287331 Flatten[Position[s, 0]] (* A287332 *)
%t A287331 Flatten[Position[s, 1]] (* A287333 *)
%t A287331 Flatten[Position[s, 2]] (* A287334 *)
%Y A287331 Cf. A287175, A287332, A287333, A287334.
%K A287331 nonn,easy
%O A287331 1,7
%A A287331 _Clark Kimberling_, May 23 2017
%E A287331 Definition corrected by _Georg Fischer_, May 27 2021