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A287345
2-limiting word of the morphism 0->11, 1->20, 2->0.
6
2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 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, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 0
OFFSET
1,1
COMMENTS
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 2-limiting word is the limit of the words for which the number of iterations congruent to 2 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}.
LINKS
EXAMPLE
2nd iterate: 2020
5th iterate: 20200110112020011011
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {2, 0}, 2 -> 0}] &, {0}, 11] (* A287345 *)
Flatten[Position[s, 0]] (* A287346 *)
Flatten[Position[s, 1]] (* A287347 *)
Flatten[Position[s, 2]] (* A287348 *)
CROSSREFS
Cf. A287337 (0-limiting word), A287341 (1-limiting word), A287346, A287347, A287348.
Sequence in context: A237584 A254886 A030219 * A260675 A035147 A101673
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 24 2017
STATUS
approved