A162648 - OEIS

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A162648

Locations of patterns 1001 or 0110 in the Thue-Morse sequence A010060.

0, 4, 6, 8, 12, 16, 20, 22, 24, 28, 30, 32, 36, 38, 40, 44, 48, 52, 54, 56, 60, 64, 68, 70, 72, 76, 80, 84, 86, 88, 92, 94, 96, 100, 102, 104, 108, 112, 116, 118, 120, 124, 126, 128, 132, 134, 136, 140, 144, 148, 150, 152, 156, 158, 160, 164, 166, 168, 172, 176, 180

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Numbers n for which A010060(n+1) = A010060(n+2) = 1-A010060(n) and A010060(n+3) = A010060(n).

Or intersection of A121539, A161674, and A161579.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A079523(n) - 1.

MATHEMATICA

Select[Range[3500], MatchQ[IntegerDigits[#, 2], {b : (1) ..} | {___, 0, b : (1) ..} /; OddQ[Length[{b}]]] &] - 1 (* G. C. Greubel, Jan 05 2018 *)

With[{nn=200}, Sort[Join[SequencePosition[ThueMorse[Range[0, nn]], {1, 0, 0, 1}], SequencePosition[ ThueMorse[Range[0, nn]], {0, 1, 1, 0}]]][[;; , 1]]]-1 (* Harvey P. Dale, Aug 20 2024 *)

PROG

(PARI) is(n)=my(v=vector(4, i, hammingweight(n+i-1))); v[1]==v[4] && v[1]!=v[2] && v[1]!=v[3] \\ Charles R Greathouse IV, Aug 20 2013

CROSSREFS

Cf. A161824, A161817, A161674, A161673, A161639, A161641, A161627, A161579, A161580, A121539, A131323, A036554, A010060, A079523, A081706.

Sequence in context: A097619 A113709 A076082 * A225512 A233036 A062554

Adjacent sequences: A162645 A162646 A162647 * A162649 A162650 A162651

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Jul 08 2009

EXTENSIONS

More readable definition from R. J. Mathar, Sep 16 2009

STATUS

approved