A287123 -id:A287123

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A287121

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

+10
5

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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}.

LINKS

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

EXAMPLE

2nd iterate: 2010

4th iterate: 2020101102010

6th iterate: 202010202010110201011011020102020101102010

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 *)

CROSSREFS

Cf. A287122, A287123, A287124, A287129.

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 22 2017

STATUS

approved

A287122

Positions of 0 in A287121.

+10
4

2, 4, 6, 8, 10, 12, 15, 17, 19, 21, 23, 25, 27, 29, 31, 34, 36, 38, 41, 44, 46, 48, 50, 52, 54, 57, 59, 61, 63, 65, 67, 69, 71, 73, 76, 78, 80, 82, 84, 86, 88, 90, 92, 95, 97, 99, 102, 105, 107, 109, 111, 113, 115, 118, 120, 122, 125, 128, 130, 132, 135, 138

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

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 *)

CROSSREFS

Cf. A287121, A287123, A287124.

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 22 2017

STATUS

approved

A287124

Positions of 2 in A287121.

+10
4

1, 3, 7, 9, 16, 20, 22, 26, 28, 35, 45, 49, 51, 58, 62, 64, 68, 70, 77, 81, 83, 87, 89, 96, 106, 110, 112, 119, 129, 139, 143, 145, 152, 156, 158, 162, 164, 171, 181, 185, 187, 194, 198, 200, 204, 206, 213, 217, 219, 223, 225, 232, 242, 246, 248, 255, 259

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 1}] &, {0}, 12] (* A287121 *)

Flatten[Position[s, 0]] (* A287122 *)

Flatten[Position[s, 1]] (* A287123 *)

Flatten[Position[s, 2]] (* A287124 *)

CROSSREFS

Cf. A287121, A287122, A287123.

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 22 2017

STATUS

approved

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