A287321 -id:A287321 - cp's OEIS frontend

A287320 0-limiting word of the morphism 0->10, 1->22, 2->0.

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

Offset: 1

Clark Kimberling, May 23 2017

Starting with 0, the first 5 iterations of the morphism yield words shown here:
  1st: 10
  2nd: 2210
  3rd: 002210
  4th: 1010002210
  5th: 221022101010002210
The 0-limiting word is the limit of the words for which the number of iterations is congruent to 0 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 = 2.28537528186132044169516884721360670506...,
  V = 3.87512979416277882597397059430967806752...,
  W = 3.28537528186132044169516884721360670506...
If n >= 2, then u(n) - u(n-1) is in {1,2,4}, v(n) - v(n-1) is in {2,4,6}, and w(n) - w(n-1) is in {1,3,5,9}.

			3rd iterate: 002210
6th iterate: 002210002210221022101010002210

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

Cf. A287321, A287322, A287323, A287181. A298200.

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 12] (* A287320 *)
Flatten[Position[s, 0]] (* A287321 *)
Flatten[Position[s, 1]] (* A287322 *)
Flatten[Position[s, 2]] (* A287323 *)
SubstitutionSystem[{0->{1,0},1->{2,2},2->{0}},{2},{10}][[1]] (* Harvey P. Dale, Aug 17 2022 *)

A287322 Positions of 1 in A287320.

Original entry on oeis.org

5, 11, 15, 19, 21, 23, 29, 35, 41, 45, 49, 51, 53, 59, 63, 67, 69, 71, 77, 81, 85, 87, 89, 95, 97, 99, 105, 107, 109, 115, 121, 127, 131, 135, 137, 139, 145, 151, 157, 161, 165, 167, 169, 175, 181, 187, 191, 195, 197, 199, 205, 209, 213, 215, 217, 223, 227

Offset: 1

Clark Kimberling, May 23 2017

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

Cf. A287320, A287321, A287323.

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 9] (* A287175 *)
Flatten[Position[s, 0]] (* A287321 *)
Flatten[Position[s, 1]] (* A287322 *)
Flatten[Position[s, 2]] (* A287323 *)

A287323 Positions of 2 in A287320.

Original entry on oeis.org

3, 4, 9, 10, 13, 14, 17, 18, 27, 28, 33, 34, 39, 40, 43, 44, 47, 48, 57, 58, 61, 62, 65, 66, 75, 76, 79, 80, 83, 84, 93, 94, 103, 104, 113, 114, 119, 120, 125, 126, 129, 130, 133, 134, 143, 144, 149, 150, 155, 156, 159, 160, 163, 164, 173, 174, 179, 180, 185

Offset: 1

Clark Kimberling, May 23 2017

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

Cf. A287320, A287321, A287322.

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 9] (* A287175 *)
Flatten[Position[s, 0]] (* A287321 *)
Flatten[Position[s, 1]] (* A287322 *)
Flatten[Position[s, 2]] (* A287323 *)

cp's OEIS Frontend

A287320 0-limiting word of the morphism 0->10, 1->22, 2->0.

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A287322 Positions of 1 in A287320.

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A287323 Positions of 2 in A287320.

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