A156659 Characteristic function of safe primes.

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

Offset: 0

Author

Reinhard Zumkeller, Feb 13 2009

Keywords

• nonn

Links

• R. Zumkeller, Table of n, a(n) for n = 0..10000
• Wikipedia, Safe prime
• Index entries for characteristic functions

Crossrefs

Cf. A005385, A156660, A292936.

Programs

Haskell

a156659 n = fromEnum $ a010051 n == 1 && a010051 (n `div` 2) == 1
-- Reinhard Zumkeller, Sep 18 2011

Mathematica

Array[Boole[And[PrimeQ@ #, PrimeQ[(# - 1)/2]]] &, 105, 0] (* Michael De Vlieger, Dec 16 2017 *)

PARI

a(n) = isprime(n) && isprime(floor((n-1)/2)) \\ Iain Fox, Dec 17 2017

Formula

a(n) = if n and also (n-1)/2 is prime then 1 else 0;

a(A005385(n)) = 1; a(A156657(n)) = 0; a(A059456(n)) = 0.

a(n) = A010051(n)*A010051((n-1)/2).

A156875(n) = Sum_{k=1..n} a(k). - Reinhard Zumkeller, Feb 18 2009

a(n) = 1 iff A292936(n) > 1. - Antti Karttunen, Dec 15 2017