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A287200 2-limiting word of the morphism 0->10, 1->20, 2->1. 4
2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Starting with 0, the first 5 iterations of the morphism yield words shown here:

1st:  10

2nd:  2210

3rd:  002210

4th:  1010002210

5th:  221022101010002210

The 2-limiting word is the limit of the words for which the number of iterations is 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 = 2.28537528186132044169516884721360670506...,

V = 3.87512979416277882597397059430967806752...,

W = 3.28537528186132044169516884721360670506...

If n >=2, then u(n) - u(n-1) is in {1,2,4}, v(n) - v(n-1) is in {2,4,6}, and w(n) - w(n-1) is in {1,3,5,9}.

LINKS

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

EXAMPLE

2nd iterate: 2210

5th iterate: 221022101010002210

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 11] (* A287200 *)

Flatten[Position[s, 0]] (* A287201 *)

Flatten[Position[s, 1]] (* A287202 *)

Flatten[Position[s, 2]] (* A287203 *)

CROSSREFS

Cf. A287175, A287179, A287201, A287202.

Sequence in context: A141647 A001617 A282947 * A284387 A143667 A246785

Adjacent sequences:  A287197 A287198 A287199 * A287201 A287202 A287203

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 23 2017

STATUS

approved

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Last modified February 21 12:10 EST 2018. Contains 299411 sequences. (Running on oeis4.)