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A287337
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0-limiting word of the morphism 0->11, 1->20, 2->0.
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6
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0, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1
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OFFSET
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1,9
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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: 2020
3rd: 011011
4th: 112020112020
5th: 20200110112020011011
The 0-limiting word is the limit of the words for which the number of iterations 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 = 2.7692923542386314152404094643350334926...,
V = 2.4498438945029551040577327454145475624...,
W = 4.3344900716222708116779374775820643087...
If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,5,6,10}, and w(n) - w(n-1) is in {2,4,8,10,16}.
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LINKS
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EXAMPLE
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3rd iterate: 011011
6th iterate: 011011112020112020011011112020112020
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MATHEMATICA
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s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {2, 0}, 2 -> 0}] &, {0}, 12] (* A287337 *)
Flatten[Position[s, 0]] (* A287338 *)
Flatten[Position[s, 1]] (* A287339 *)
Flatten[Position[s, 2]] (* A287340 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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