A287157 -id:A287157 - cp's OEIS frontend

A287156 2-limiting word of the morphism 0->10, 1->21, 2->0.

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

Offset: 1

Clark Kimberling, May 22 2017

Starting with 0, the first 4 iterations of the morphism yield words shown here:
1st:  10
2nd:  2110
3rd:  0212110
4th:  1002010212110
The 2-limiting word is the limit of the words for which the number of iterations is congruent to 2 mod 3.
Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2.  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 = 3.079595623491438786010417...,
V = 2.324717957244746025960908...,
W = U + 1 = 4.079595623491438786010417....
If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,3,4}, and w(n) - w(n-1) is in {2,3,4,5,7}.

			The 2nd, 5th, and 8th iterates are 2110, 211010021100210212110, 211010021100210212110100210212110021211021101002110021021211002121102110100210212110211010021211010021100210212110.

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

Cf. A287108, A287157, A287158, A287159, A297160.

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 11]   (* A287156 *)
Flatten[Position[s, 0]] (* A287157 *)
Flatten[Position[s, 1]] (* A287158 *)
Flatten[Position[s, 2]] (* A287159 *)

A287158 Positions of 1 in A287156.

Original entry on oeis.org

2, 3, 5, 9, 10, 14, 17, 19, 20, 22, 26, 29, 31, 32, 36, 38, 39, 42, 43, 45, 49, 50, 54, 57, 59, 60, 64, 66, 67, 70, 71, 73, 77, 80, 82, 83, 86, 87, 89, 93, 95, 96, 98, 102, 103, 107, 110, 112, 113, 115, 119, 122, 124, 125, 129, 131, 132, 135, 136, 138, 142

Offset: 1

Clark Kimberling, May 22 2017

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

Cf. A287108, A287156, A287157, A287159.

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 11] (* A287156 *)
Flatten[Position[s, 0]] (* A287157 *)
Flatten[Position[s, 1]] (* A287158 *)
Flatten[Position[s, 2]] (* A287159 *)

A287159 Positions of 2 in A287156.

Original entry on oeis.org

1, 8, 13, 16, 18, 25, 28, 30, 35, 37, 41, 48, 53, 56, 58, 63, 65, 69, 76, 79, 81, 85, 92, 94, 101, 106, 109, 111, 118, 121, 123, 128, 130, 134, 141, 144, 146, 150, 157, 159, 166, 171, 174, 176, 181, 183, 187, 194, 196, 203, 208, 211, 213, 217, 224, 229, 232

Offset: 1

Clark Kimberling, May 22 2017

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

Cf. A287108, A287156, A287157, A287158.

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 11] (* A287156 *)
Flatten[Position[s, 0]] (* A287157 *)
Flatten[Position[s, 1]] (* A287158 *)
Flatten[Position[s, 2]] (* A287159 *)

cp's OEIS Frontend

A287156 2-limiting word of the morphism 0->10, 1->21, 2->0.

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A287158 Positions of 1 in A287156.

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A287159 Positions of 2 in A287156.

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