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A248057 Positions of 1,1 in the Thue-Morse sequence (A010060). 4
2, 8, 14, 22, 26, 32, 38, 42, 50, 56, 62, 70, 74, 82, 88, 94, 98, 104, 110, 118, 122, 128, 134, 138, 146, 152, 158, 162, 168, 174, 182, 186, 194, 200, 206, 214, 218, 224, 230, 234, 242, 248, 254, 262, 266, 274, 280, 286, 290, 296, 302, 310, 314, 322, 328 (list; graph; refs; listen; history; text; internal format)
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*A091855(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) = 2 and a(2) = 8.

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]], {1, 1}][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 16 2017 *)

CROSSREFS

Cf. A010060, A091855, A091785, A248056.

Sequence in context: A064148 A161464 A211873 * A121055 A107072 A120413

Adjacent sequences:  A248054 A248055 A248056 * A248058 A248059 A248060

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 30 2014

STATUS

approved

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Last modified October 14 04:44 EDT 2019. Contains 327995 sequences. (Running on oeis4.)