A192611 Primes prime(k) such that prime(k)*k+1 is also prime.

2, 3, 7, 13, 89, 113, 151, 181, 359, 433, 521, 541, 641, 701, 719, 827, 953, 1033, 1277, 1301, 1439, 1877, 2069, 2111, 2143, 2267, 2357, 2423, 2791, 2801, 2861, 2887, 3191, 3251, 3313, 3557, 3643, 3739, 3797, 3821, 3863, 3931, 3947, 4021, 4447

Offset: 1

Author

Andrea Raffetti, Jul 05 2011

Keywords

• nonn

Comments

Primes p such that p*pi(p)+1 is prime (see Crossrefs).

Examples

			13 is in the list because, being the 6th prime, 13*6+1=79 is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A096064, A086172.

Cf. A000040 The prime numbers.

Cf. A000720 pi(n), the number of primes <= n.

Programs

Magma

[ NthPrime(n): n in [1..650] | IsPrime(NthPrime(n)*n+1) ]; // Bruno Berselli, Jul 05 2011

Mathematica

Select[Prime[Range[700]],PrimeQ[# PrimePi[#]+1]&] (* Harvey P. Dale, May 28 2012 *)

PARI

k=0;forprime(p=2,1e4,if(isprime(k++*p+1),print1(p", "))) \\ Charles R Greathouse IV, Jul 05 2011