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A287156
2-limiting word of the morphism 0->10, 1->21, 2->0.
5
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, 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, 0, 2, 1, 2, 1, 1, 0, 2, 1
OFFSET
1,1
COMMENTS
Starting with 0, the first 4 iterations of the morphism yield words shown here:
1st: 10
2nd: 2110
3rd: 0212110
4th: 1002010212110
The 2-limiting word is the limit of the words for which the number of iterations is congruent to 2 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 2nd, 5th, and 8th iterates are 2110, 211010021100210212110, 211010021100210212110100210212110021211021101002110021021211002121102110100210212110211010021211010021100210212110.
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 11] (* A287156 *)
Flatten[Position[s, 0]] (* A287157 *)
Flatten[Position[s, 1]] (* A287158 *)
Flatten[Position[s, 2]] (* A287159 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 22 2017
STATUS
approved