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

0,1

Links

R. Zumkeller, Table of n, a(n) for n = 0..10000

Wikipedia, Safe prime

Index entries for characteristic functions

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

Mathematica

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

Prog

(Haskell)
a156659 n = fromEnum $ a010051 n == 1 && a010051 (n `div` 2) == 1
-- Reinhard Zumkeller, Sep 18 2011
(PARI) a(n) = isprime(n) && isprime(floor((n-1)/2)) \\ Iain Fox, Dec 17 2017

Crossrefs

Cf. A005385, A156660, A292936.

Sequence in context: A202238 A144194 A144196 * A011671 A086483 A337383

Adjacent sequences: A156656 A156657 A156658 * A156660 A156661 A156662

Keyword

nonn

Author

Reinhard Zumkeller, Feb 13 2009

Status

approved