A287174 2-limiting word of the morphism 0->10, 1->20, 2->0.

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

Offset: 1

Author

Clark Kimberling, May 22 2017

Keywords

• nonn
• easy

Comments

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

1st: 10

2nd: 2010

3rd: 0102010

4th: 1020100102010

5th: 201001020101020100102010

The 2-limiting word is the limit of the words for which the number of iterations is congruent to 2 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 = 1.8392867552141611325518525646532866...,

V = U^2 = 3.3829757679062374941227085364...,

W = U^3 = 6.2222625231203986266745611011....

If n >=2, then u(n) - u(n-1) is in {1,2}, v(n) - v(n-1) is in {2,3,4}, and w(n) - w(n-1) is in {4,6,7}.

Examples

			2nd iterate: 2010
5th iterate: 201001020101020100102010
		

Links

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

Crossrefs

Cf. A286998, A287111, A287175, A287176, A287177.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 0}] &, {0}, 11] (* A287174 *)
Flatten[Position[s, 0]] (* A287175 *)
Flatten[Position[s, 1]] (* A287176 *)
Flatten[Position[s, 2]] (* A287177 *)