A287240 1-limiting word of the morphism 0->01, 1->20, 2->1, with initial term 1.

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

Offset

1,1

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 1-limiting word is the limit of the words for which the number of iterations is odd.

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

1st iterate: 20
3rd iterate: 200120
5th iterate: 2001200120101200120

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 0}, 2 -> 1}] &, {1}, 11] (* A287240 *)
Flatten[Position[s, 0]] (* A287241 *)
Flatten[Position[s, 1]] (* A287242 *)
Flatten[Position[s, 2]] (* A287243 *)

Crossrefs

Cf. A287002 (initial 0 instead of 2), A287234 (0-limiting word), A287241, A287242, A287243.

Sequence in context: A325189 A357637 A130731 * A025875 A026840 A357648

Adjacent sequences: A287237 A287238 A287239 * A287241 A287242 A287243

Keyword

nonn,easy

Author

Clark Kimberling, May 24 2017

Status

approved