A248104 - OEIS

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

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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)

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 *)