A248105 - OEIS

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

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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