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

Author

Clark Kimberling, Oct 01 2014

Keywords

• nonn
• easy

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)

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)