A248105 Positions of 1,0,1 in the Thue-Morse sequence (A010060).

3, 12, 15, 20, 27, 36, 43, 48, 51, 60, 63, 68, 75, 80, 83, 92, 99, 108, 111, 116, 123, 132, 139, 144, 147, 156, 163, 172, 175, 180, 187, 192, 195, 204, 207, 212, 219, 228, 235, 240, 243, 252, 255, 260, 267, 272, 275, 284, 291, 300, 303, 308, 315, 320, 323

Offset

1,1

Comments

Every positive integer lies in exactly one of these six sequences:

A248056 (positions of 0,0,1)

A248104 (positions of 0,1,0)

A157970 (positions of 1,0,0)

A157971 (positions of 0,1,1)

A248105 (positions of 1,0,1)

A248057 (positions of 1,1,0)

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

Thue-Morse sequence:  0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,..., so that a(1) = 3 and a(2) = 12.

Mathematica

z = 600; u = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 13]; v = Rest[u]; w = Rest[v]; t1 = Table[If[u[[n]] == 0 && v[[n]] == 0 && w[[n]] == 1, 1, 0], {n, 1, z}];
t2 = Table[If[u[[n]] == 0 && v[[n]] == 1 && w[[n]] == 0, 1, 0], {n, 1, z}];
t3 = Table[If[u[[n]] == 1 && v[[n]] == 0 && w[[n]] == 0, 1, 0], {n, 1, z}];
t4 = Table[If[u[[n]] == 0 && v[[n]] == 1 && w[[n]] == 1, 1, 0], {n, 1, z}];
t5 = Table[If[u[[n]] == 1 && v[[n]] == 0 && w[[n]] == 1, 1, 0], {n, 1, z}];
t6 = Table[If[u[[n]] == 1 && v[[n]] == 1 && w[[n]] == 0, 1, 0], {n, 1, z}];
Flatten[Position[t1, 1]]  (* A248056 *)
Flatten[Position[t2, 1]]  (* A248104 *)
Flatten[Position[t3, 1]]  (* A157970 *)
Flatten[Position[t4, 1]]  (* A157971 *)
Flatten[Position[t5, 1]]  (* A248105 *)
Flatten[Position[t6, 1]]  (* A248057 *)

Crossrefs

Cf. A010060, A248056, A157970, A157971, A248104, A248057.

Sequence in context: A188549 A287357 A044828 * A269315 A329575 A022380

Adjacent sequences: A248102 A248103 A248104 * A248106 A248107 A248108

Keyword

nonn,easy

Author

Clark Kimberling, Oct 01 2014

Status

approved