A373157 a(n) = 1 if the 2-adic valuation of n is a multiple of 3, otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions.

Formula

Multiplicative with a(p^e) = 1 if e is a multiple of 3, or p > 2, otherwise 0.

a(n) = [A007814(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

a(n) = [A191255(n) = 0 or 3].

Sum_{k=1..n} a(k) ~ (4/7) * n. - Amiram Eldar, May 31 2024

Mathematica

a[n_] := If[Divisible[IntegerExponent[n, 2], 3], 1, 0]; Array[a, 100] (* Amiram Eldar, May 31 2024 *)

Prog

(PARI) A373157(n) = !(valuation(n, 2)%3);

Crossrefs

Characteristic function of A191257.

Cf. A001511, A007814, A191255.

Sequence in context: A195062 A351077 A229940 * A179761 A317906 A102863

Adjacent sequences: A373154 A373155 A373156 * A373158 A373159 A373160

Keyword

nonn,mult,easy

Author

Antti Karttunen, May 28 2024

Status

approved