A099618 a(n) = 1 if the n-th prime == 1 mod 6, otherwise a(n) = 0.

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

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 19 2004

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for characteristic functions.

Crossrefs

Characteristic function of A091178.

Cf. A000040, A039704, A132194.

Programs

Mathematica

Table[Mod[Mod[Mod[Mod[Prime[k], 6], 5], 3], 2], {k, 1, 120}]
a[n_] := Boole[Mod[Prime[n], 6] == 1]; Array[a, 120] (* Amiram Eldar, Mar 14 2025 *)

PARI

a(n) = (prime(n) % 6) == 1; \\ Michel Marcus, Jun 26 2019

Formula

From Amiram Eldar, Mar 14 2025: (Start)

a(n) = 1 - A132194(m).

Sum_{k=1..n} a(k) ~ n / 2. (End)