A287331 1-limiting word of the morphism 0->10, 1->22, 2->0, starting with 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, 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

Offset

1,7

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

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

1st iterate: 10
4th iterate: 1010002210

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 10] (* A287331 *)
Flatten[Position[s, 0]] (* A287332 *)
Flatten[Position[s, 1]] (* A287333 *)
Flatten[Position[s, 2]] (* A287334 *)

Crossrefs

Cf. A287175, A287332, A287333, A287334.

Sequence in context: A347687 A368948 A368579 * A179769 A340594 A361685

Adjacent sequences: A287328 A287329 A287330 * A287332 A287333 A287334

Keyword

nonn,easy

Author

Clark Kimberling, May 23 2017

Extensions

Definition corrected by Georg Fischer, May 27 2021

Status

approved