A051686 Smallest prime p such that 2n*p+1 is also prime.

2, 3, 2, 2, 3, 3, 2, 7, 2, 2, 3, 3, 2, 7, 2, 3, 3, 2, 5, 7, 3, 2, 3, 2, 2, 3, 2, 2, 19, 3, 5, 3, 3, 2, 3, 13, 2, 3, 2, 3, 19, 5, 2, 7, 2, 3, 3, 2, 2, 7, 3, 3, 7, 5, 3, 3, 2, 2, 7, 2, 3, 3, 3, 2, 7, 3, 2, 3, 2, 2, 13, 3, 2, 37, 5, 3, 3, 2, 2, 13, 3, 5, 3, 2, 11, 13, 2, 2, 31, 3, 3, 7, 2, 5, 3, 3, 2, 7, 2, 2

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

These are the primes arising in A051899.

Examples

			a(29)=19 because 19 is the smallest prime p such that 2*29*p+1 is prime.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005384, A051644-A051654, A051899.

Programs

Mathematica

Table[k = 1; While[! PrimeQ[2 n Prime@ k + 1], k++]; Prime@ k, {n, 120}] (* Michael De Vlieger, Jul 26 2016 *)

PARI

a(n) = p=2; while(!isprime(2*n*p+1), p = nextprime(p+1)); p; \\ Michel Marcus, Dec 10 2013