A248104 Positions of 0,1,0 in the Thue-Morse sequence (A010060).

4, 11, 16, 19, 28, 35, 44, 47, 52, 59, 64, 67, 76, 79, 84, 91, 100, 107, 112, 115, 124, 131, 140, 143, 148, 155, 164, 171, 176, 179, 188, 191, 196, 203, 208, 211, 220, 227, 236, 239, 244, 251, 256, 259, 268, 271, 276, 283, 292, 299, 304, 307, 316, 319, 324

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)

The terms of the sequence are the positions of the mean of the positions of the three numbers 0, 1, 0. - Harvey P. Dale, Jan 26 2019

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) = 4 and a(2) = 11.

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 *)
Mean/@SequencePosition[ThueMorse[Range[400]], {0, 1, 0}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 26 2019 *)

Crossrefs

Cf. A010060, A248056, A157970, A157971, A248105, A248057.

Sequence in context: A330338 A193587 A261155 * A072423 A310558 A310559

Adjacent sequences: A248101 A248102 A248103 * A248105 A248106 A248107

Keyword

nonn,easy

Author

Clark Kimberling, Oct 01 2014

Status

approved