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A287360
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0-limiting word of the morphism 0->11, 1->21, 2->0.
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6
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0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0
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OFFSET
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1,2
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COMMENTS
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Starting with 0, the first 5 iterations of the morphism yield words shown here:
1st: 11
2nd: 2121
3rd: 021021
4th: 1102111021
5th: 212111021212111021
The 0-limiting word is the limit of the words for which the number of iterations is congruent to 0 mod 3.
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
U = 5.5707505637226408833903376944272134...,
V = 1.9375648970813894129869852971548390...,
W = 3.2853752818613204416951688472136067...
If n >=2, then u(n) - u(n-1) is in {3,5,9}, v(n) - v(n-1) is in {1,2,3}, and w(n) - w(n-1) is in {2,3,5}.
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..10000
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EXAMPLE
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3rd iterate: 021021
6th iterate: 021021212111021021021212111021
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MATHEMATICA
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s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 12] (* A287360 *)
Flatten[Position[s, 0]] (* A287361 *)
Flatten[Position[s, 1]] (* A287362 *)
Flatten[Position[s, 2]] (* A287363 *)
SubstitutionSystem[{0->{1, 1}, 1->{2, 1}, 2->{0}}, {0}, {9}][[1]] (* Harvey P. Dale, Dec 04 2022 *)
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CROSSREFS
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Cf. A287361, A287362, A287363, A287364 (1-limiting word);, A287368 (2-limiting word).
Sequence in context: A190427 A287108 A333948 * A035443 A180430 A246369
Adjacent sequences: A287357 A287358 A287359 * A287361 A287362 A287363
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, May 24 2017
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STATUS
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approved
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