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A287160 0-limiting word of the morphism 0->10, 1->21, 2->0. 4
0, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 2, 1, 2, 1, 1, 0, 1, 0, 0, 2, 1, 1, 0, 0, 2, 1, 0, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 2, 1, 1, 0, 0, 2, 1, 0, 2, 1, 2, 1, 1, 0, 1, 0, 0, 2, 1, 0, 2, 1, 2, 1, 1, 0, 0, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Starting with 0, the first 4 iterations of the morphism yield words shown here:
1st: 10
2nd: 2110
3rd: 0212110
4th: 1002010212110
The 0-limiting word is the limit of the words for which the number of iterations is congruent to 0 mod 3.
Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2. 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 = 3.079595623491438786010417...,
V = 2.324717957244746025960908...,
W = U + 1 = 4.079595623491438786010417....
If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,3,4}, and w(n) - w(n-1) is in {2,3,4,5,7}.
LINKS
EXAMPLE
The 3rd and 6th iterates are 0212110 and 0212110211010021211010021100210212110.
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 9] (* A287160 *)
Flatten[Position[s, 0]] (* A287161 *)
Flatten[Position[s, 1]] (* A287162 *)
Flatten[Position[s, 2]] (* A287163 *)
CROSSREFS
Sequence in context: A117118 A117168 A355343 * A029443 A078508 A029416
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 22 2017
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)