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A293162 Take every third term of the {0,1}-version of the Thue-Morse sequence: a(n) = A010060(3n). 6
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0
COMMENTS
a(2n) = a(n). This is because the binary weight of 2(3n) is the same as the binary weight of 3n.
Characteristic sequence of A036556. Run lengths are A026497. - Andrey Zabolotskiy, Dec 31 2023
LINKS
Alan Cobham, Uniform tag sequences, Math. Systems Theory (1972) 6: 164-192. See Example 9.
Roswitha Hofer, Coquet-type formulas for the rarefied weighted Thue-Morse sequence Discrete Mathematics 311.16 (2011): 1724-1734.
FORMULA
From Antti Karttunen, Dec 01 2017: (Start)
a(n) = A000120(3*n) mod 2.
a(n) = A010060(n) + A295890(n) mod 2. (End)
a(n) = A026492(n) - 1. - Andrey Zabolotskiy, Dec 31 2023
MATHEMATICA
ThueMorse[Range[0, 300, 3]] (* Paolo Xausa, Dec 18 2023 *)
PROG
(Scheme) (define (A293162 n) (A000035 (A000120 (* 3 n)))) ;; Antti Karttunen, Dec 01 2017
CROSSREFS
Sequence in context: A295659 A188436 A037823 * A115790 A025460 A169673
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 15 2017
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)