A287234 0-limiting word of the morphism 0->01, 1->20, 2->1, with initial term 1.

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

Offset

1,6

Comments

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

1st: 20

2nd: 101

3rd: 200120

4th: 1010120101

5th: 2001200120101200120

The 0-limiting word is the limit of the words for which the number of iterations is even.

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 = 2.246979603717467061050009768008...,

V = 2.801937735804838252472204639014...,

W = 5.048917339522305313522214407023...

If n >=2, then u(n) - u(n-1) is in {1,2,3}, v(n) - v(n-1) is in {2,3,4}, and w(n) - w(n-1) is in {4,5,7}.

Links

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

Example

2nd iterate: 101
4th iterate: 1010120101
6th iterate: 101012010101201012001201010120101

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 0}, 2 -> 1}] &, {1}, 10] (* A287234 *)
Flatten[Position[s, 0]] (* A287235 *)
Flatten[Position[s, 1]] (* A287236 *)
Flatten[Position[s, 2]] (* A287237 *)

Crossrefs

Cf. A287002 (initial 0 instead of 1), A287235, A287236, A287237, A287240 (1-limiting word).

Sequence in context: A364389 A116927 A137276 * A309938 A140581 A137277

Adjacent sequences: A287231 A287232 A287233 * A287235 A287236 A287237

Keyword

nonn,easy

Author

Clark Kimberling, May 23 2017

Status

approved