A248056 Positions of 0,0 in the Thue-Morse sequence (A010060).

6, 10, 18, 24, 30, 34, 40, 46, 54, 58, 66, 72, 78, 86, 90, 96, 102, 106, 114, 120, 126, 130, 136, 142, 150, 154, 160, 166, 170, 178, 184, 190, 198, 202, 210, 216, 222, 226, 232, 238, 246, 250, 258, 264, 270, 278, 282, 288, 294, 298, 306, 312, 318, 326, 330

Offset

1,1

Comments

Every positive integer lies in exactly one of these four sequences: A248056, A091855, A091855, A248057.

Links

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

Formula

a(n) = 2*A091785(n) for n >= 1.

Example

Thue-Morse sequence:  0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,..., so that a(1) = 6 and a(2) = 10.

Mathematica

z = 400; u = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* A010060 *)
v = Rest[u]
t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
Flatten[Position[t1, 1]]  (* A248056 *)
Flatten[Position[t2, 1]]  (* A091855 *)
Flatten[Position[t3, 1]]  (* A091785 *)
Flatten[Position[t4, 1]]  (* A248057 *)
SequencePosition[ThueMorse[Range[400]], {0, 0}][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 02 2020 *)

Crossrefs

Cf. A010060, A091855, A091785, A248057.

Sequence in context: A315364 A315365 A315366 * A331861 A032641 A293555

Adjacent sequences: A248053 A248054 A248055 * A248057 A248058 A248059

Keyword

nonn,easy

Author

Clark Kimberling, Sep 30 2014

Status

approved