A295890 a(n) = 1 if binary weights of n and 3n have different parity, 0 otherwise; a(n) = A010060(n) XOR A010060(3n).

0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0

Offset

0

Comments

Thue-Morse sequence A010060(n) xored with its trisection, A293162(n) = A010060(3n).

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to binary expansion of n.

Index entries for characteristic functions.

Formula

a(n) = (A000120(n) + A000120(3*n)) mod 2.

a(n) = A010060(n) + A293162(n) mod 2.

a(n) = 1 - A295889(n).

a(A003714(n)) = A095076(n).

For n >= 1, a(A003961(n)) = abs(A295891(n) - A295891(2*n)).

Mathematica

a[n_] := If[Mod[DigitCount[n, 2, 1], 2] == Mod[DigitCount[3*n, 2, 1], 2], 0, 1]; Array[a, 100, 0] (* Amiram Eldar, Feb 07 2023 *)

Prog

(Scheme) (define (A295890 n) (A000035 (+ (A000120 n) (A000120 (* 3 n)))))

Crossrefs

Cf. A000035, A000120, A010060, A293162, A295889, A295891.

Cf. also A003714, A095076.

Sequence in context: A029691 A209229 A365089 * A342704 A284622 A379184

Adjacent sequences: A295887 A295888 A295889 * A295891 A295892 A295893

Keyword

nonn,base

Author

Antti Karttunen, Nov 30 2017

Status

approved