A248056 - OEIS

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A248056

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

4

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

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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