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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 (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:  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

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

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

Adjacent sequences:  A287342 A287343 A287344 * A287346 A287347 A287348

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 24 2017

STATUS

approved

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Last modified May 17 06:41 EDT 2022. Contains 353730 sequences. (Running on oeis4.)