A287341 1-limiting word of the morphism 0->11, 1->20, 2->0.

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, 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, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 0, 1

Offset

1,3

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

3rd iterate: 011011
6th iterate: 011011112020112020011011112020112020

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {2, 0}, 2 -> 0}] &, {0}, 10] (* A287341 *)
Flatten[Position[s, 0]] (* A287342 *)
Flatten[Position[s, 1]] (* A287343 *)
Flatten[Position[s, 2]] (* A287344 *)

Crossrefs

Cf. A287337 (0-limiting word), A287342, A287343, A287344, A287345 (2-limiting word).

Sequence in context: A264049 A287337 A026612 * A282432 A046922 A193779

Adjacent sequences: A287338 A287339 A287340 * A287342 A287343 A287344

Keyword

nonn,easy

Author

Clark Kimberling, May 24 2017

Status

approved