A287069 -id:A287069 - cp's OEIS frontend

A287066 Start with 1 and repeatedly substitute 0->01, 1->12, 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, 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, 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

Offset: 1

Clark Kimberling, May 20 2017

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

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

Cf. A057985, A287067, A287068, A287069.

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> 0}] &, {1}, 10] (* A287066 *)
Flatten[Position[s, 0]]  (* A287067 *)
Flatten[Position[s, 1]]  (* A287068 *)
Flatten[Position[s, 2]]  (* A287069 *)

A287067 Positions of 0 in A287066.

Original entry on oeis.org

3, 4, 6, 10, 16, 17, 23, 26, 27, 29, 35, 38, 39, 43, 44, 46, 50, 56, 59, 60, 64, 65, 67, 73, 74, 76, 80, 86, 87, 93, 96, 97, 101, 102, 104, 110, 111, 113, 117, 123, 126, 127, 129, 133, 139, 140, 146, 149, 150, 152, 158, 161, 162, 166, 167, 169, 175, 176, 178

Offset: 1

Clark Kimberling, May 21 2017

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

Cf. A287066, A287068, A287069.

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> 0}] &, {1}, 10] (* A287066 *)
Flatten[Position[s, 0]]  (* A287067 *)
Flatten[Position[s, 1]]  (* A287068 *)
Flatten[Position[s, 2]]  (* A287069 *)

A287068 Positions of 1 in A287066.

Original entry on oeis.org

1, 5, 7, 8, 11, 12, 14, 18, 19, 21, 24, 28, 30, 31, 33, 36, 40, 41, 45, 47, 48, 51, 52, 54, 57, 61, 62, 66, 68, 69, 71, 75, 77, 78, 81, 82, 84, 88, 89, 91, 94, 98, 99, 103, 105, 106, 108, 112, 114, 115, 118, 119, 121, 124, 128, 130, 131, 134, 135, 137, 141

Offset: 1

Clark Kimberling, May 21 2017

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

Cf. A287066, A287067, A287069.

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> 0}] &, {1}, 10] (* A287066 *)
Flatten[Position[s, 0]]  (* A287067 *)
Flatten[Position[s, 1]]  (* A287068 *)
Flatten[Position[s, 2]]  (* A287069 *)

cp's OEIS Frontend

A287066 Start with 1 and repeatedly substitute 0->01, 1->12, 2->0.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A287067 Positions of 0 in A287066.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A287068 Positions of 1 in A287066.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica