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A287108 1-limiting word of the morphism 0->10, 1->21, 2->0. 9
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, 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, 0, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 2, 1, 2, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Starting with 0, the first 4 iterations of the morphism yield words shown here:

1st:  10

2nd:  2110

3rd:  0212110

4th:  100210212110

The 1-limiting word is the limit of the words for which the number of iterations is congruent to 1 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

Clark Kimberling, Table of n, a(n) for n = 1..10000

EXAMPLE

The 1st, 4th, and 7th iterates are

10, 100210212110, 10021021211002121102110100210212110211010021211010021100210212110.

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 10] (* A287108 *)

Flatten[Position[s, 0]] (* A287109 *)

Flatten[Position[s, 1]] (* A287110 *)

Flatten[Position[s, 2]] (* A287111 *)

CROSSREFS

Cf. A287109, A287110, A287111.

Sequence in context: A130210 A236459 A190427 * A333948 A287360 A035443

Adjacent sequences:  A287105 A287106 A287107 * A287109 A287110 A287111

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 21 2017

STATUS

approved

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)