A156660 Characteristic function of Sophie Germain primes.

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

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

Crossrefs

Cf. A156659.

Cf. A005384, A156874, A092816.

Programs

Haskell

a156660 n = fromEnum $ a010051 n == 1 && a010051 (2 * n + 1) == 1
-- Reinhard Zumkeller, May 01 2012

PARI

a(n)=isprime(n)&&isprime(2*n+1) \\ Felix Fröhlich, Aug 11 2014

Formula

a(n) = if n and also 2*n+1 is prime then 1 else 0.

a(A005384(n)) = 1; a(A138887(n)) = 0; a(A053176(n)) = 0.

A156874(n) = Sum_{k=1..n} a(k). - Reinhard Zumkeller, Feb 18 2009

a(n) = A010051(n)*A010051(2*n+1).

For n>1 a(n) = floor((floor(phi(n)/(n-1)) + floor(phi(2*n+1)/(2*n)))/2). - Enrique Pérez Herrero, Apr 28 2012

For n>1 a(n) = floor(phi(2*n^2+n)/(2*n^2-2*n)). - Enrique Pérez Herrero, May 02 2012

Extensions

Definition corrected by Daniel Forgues, Aug 04 2009