A287337 0-limiting word of the morphism 0->11, 1->20, 2->0.

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, 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

Offset

1,9

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 0-limiting word is the limit of the words for which the number of iterations congruent to 0 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}, 12] (* A287337 *)
Flatten[Position[s, 0]] (* A287338 *)
Flatten[Position[s, 1]] (* A287339 *)
Flatten[Position[s, 2]] (* A287340 *)

Crossrefs

Cf. A287338, A287339, A287340, A287341 (1-limiting word), A287345 (2-limiting word).

Sequence in context: A112712 A026608 A264049 * A026612 A287341 A282432

Adjacent sequences: A287334 A287335 A287336 * A287338 A287339 A287340

Keyword

nonn,easy

Author

Clark Kimberling, May 24 2017

Status

approved