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A287179 1-limiting word of the morphism 0->10, 1->20, 2->1. 5
1, 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, 1, 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, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

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 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 {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}.

LINKS

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

EXAMPLE

1st iterate: 10

3rd iterate: 1102010

5th iterate: 110110201020201011020100

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 1}] &, {0}, 9] (* A287179 *)

Flatten[Position[s, 0]] (* A287180 *)

Flatten[Position[s, 1]] (* A287181 *)

Flatten[Position[s, 2]] (* A287182 *)

CROSSREFS

Cf. A287121, A287180, A287181, A287182.

Sequence in context: A263074 A281772 A082886 * A236511 A235924 A097304

Adjacent sequences:  A287176 A287177 A287178 * A287180 A287181 A287182

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 22 2017

STATUS

approved

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Last modified August 6 11:14 EDT 2020. Contains 336246 sequences. (Running on oeis4.)