A248057 - OEIS

A248057

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

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 *)

PROG

(PARI) t(n)=hammingweight(n)%2;

for(n=1, 500, if(t(n)==1&&t(n-1)==1, print1(n, ", "))); \\ Joerg Arndt, Mar 12 2022

CROSSREFS

Cf. A010060, A091855, A091785, A248056.

Sequence in context: A246299 A161464 A211873 * A121055 A344161 A375472

Adjacent sequences: A248054 A248055 A248056 * A248058 A248059 A248060

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 30 2014

STATUS

approved