A287121 0-limiting word of the morphism 0->10, 1->20, 2->1.

2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 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: 1102010

4th: 2020101102010

5th: 11011020102020101102010

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 {2,3}, v(n) - v(n-1) is in {1,2,4,6}, and w(n) - w(n-1) is in {2,4,7,10}.

Examples

			2nd iterate: 2010
4th iterate: 2020101102010
6th iterate: 202010202010110201011011020102020101102010
		

Links

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

Crossrefs

Cf. A287122, A287123, A287124, A287129.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 1}] &, {0}, 10] (* A287121 *)
Flatten[Position[s, 0]] (* A287122 *)
Flatten[Position[s, 1]] (* A287123 *)
Flatten[Position[s, 2]] (* A287124 *)