A293162 - OEIS

A293162

Take every third term of the {0,1}-version of the Thue-Morse sequence: a(n) = A010060(3n).

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

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OFFSET

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

Antti Karttunen, Table of n, a(n) for n = 0..21846

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.

Index entries for sequences related to binary expansion of n

Index entries for characteristic functions

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

Cf. A000035, A000120, A010060, A005599, A026492, A026497, A036556, A293163, A293164, A295890.

Sequence in context: A295659 A188436 A037823 * A115790 A025460 A374222

Adjacent sequences: A293159 A293160 A293161 * A293163 A293164 A293165

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 15 2017

STATUS

approved