A057986 -id:A057986 - cp's OEIS frontend

A057985 Start with 0 and repeatedly substitute: 0->01, 1->12, 2->0.

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

Offset: 1

Clark Kimberling, Oct 30 2000

nonn

This is the fixed point of the morphism 0->01, 1->12, 2->0 starting with 0. 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. 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}. For n >= 1, the number of terms resulting from n iterations of the morphism is A005251(n+2). - Clark Kimberling, May 20 2017.

Clark Kimberling, Table of n, a(n) for n = 1..10000
Index entries for sequences that are fixed points of mappings

Cf. A287066 (initial term 1 instead of 0).

t = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> {0}}] &, {0}, 10] (* A057985 *)
Flatten[Position[t, 0]] (* A057986 *)
Flatten[Position[t, 1]] (* A057987 *)
Flatten[Position[t, 2]] (* A057988 *)
(* Clark Kimberling, May 13 2013 *)

A057987 Positions of 1 in A057985.

Original entry on oeis.org

2, 3, 5, 8, 12, 13, 17, 19, 20, 22, 26, 28, 29, 32, 33, 35, 38, 42, 44, 45, 48, 49, 51, 55, 56, 58, 61, 65, 66, 70, 72, 73, 76, 77, 79, 83, 84, 86, 89, 93, 95, 96, 98, 101, 105, 106, 110, 112, 113, 115, 119, 121, 122, 125, 126, 128, 132, 133

Offset: 1

Clark Kimberling, Oct 30 2000

nonn

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

Cf. A057985, A057986, A057988.

A057988 Positions of 2 in A057985.

Original entry on oeis.org

4, 6, 9, 14, 21, 23, 30, 34, 36, 39, 46, 50, 52, 57, 59, 62, 67, 74, 78, 80, 85, 87, 90, 97, 99, 102, 107, 114, 116, 123, 127, 129, 134, 136, 139, 146, 148, 151, 156, 163, 167, 169, 172, 177, 184, 186, 193, 197, 199, 202, 209, 213

Offset: 1

Clark Kimberling, Oct 30 2000

nonn

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

Cf. A057985, A057986, A057987.

cp's OEIS Frontend

A057985 Start with 0 and repeatedly substitute: 0->01, 1->12, 2->0.

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A057987 Positions of 1 in A057985.

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A057988 Positions of 2 in A057985.

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