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A162648
Locations of patterns 1001 or 0110 in the Thue-Morse sequence A010060.
1
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
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
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jul 08 2009
EXTENSIONS
More readable definition from R. J. Mathar, Sep 16 2009
STATUS
approved