A287364 1-limiting word of the morphism 0->11, 1->21, 2->0.

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

Offset

1,4

Comments

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

1st: 11

2nd: 2121

3rd: 021021

4th: 1102111021

5th: 212111021212111021

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 = 5.5707505637226408833903376944272134...,

V = 1.9375648970813894129869852971548390...,

W = 3.2853752818613204416951688472136067...

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

Links

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

Example

4th iterate: 1102111021
7th iterate: 11021110210210212121110211102111021021021212111021

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 13] (* A287364 *)
Flatten[Position[s, 0]] (* A287365 *)
Flatten[Position[s, 1]] (* A287366 *)
Flatten[Position[s, 2]] (* A287367 *)

Crossrefs

Cf. A287360 (0-limiting word), A287365, A287366, A287367, A287368 (2-limiting word).

Sequence in context: A026609 A286935 A090340 * A340676 A117162 A277045

Adjacent sequences: A287361 A287362 A287363 * A287365 A287366 A287367

Keyword

nonn,easy

Author

Clark Kimberling, May 24 2017

Status

approved