A051886 a(n) is the minimal prime p such that 2^n * p + 1 is prime.

2, 2, 3, 2, 7, 3, 3, 2, 3, 23, 13, 29, 3, 5, 7, 2, 37, 53, 3, 11, 7, 11, 37, 71, 73, 5, 7, 17, 13, 23, 3, 239, 43, 113, 163, 59, 3, 89, 349, 5, 97, 3, 73, 11, 67, 101, 19, 101, 61, 23, 7, 17, 7, 233, 127, 5, 541, 29, 103, 71, 31, 53, 109, 179, 163, 71, 3, 929, 31, 23, 193, 101

Offset: 0

Author

Labos Elemer, Dec 15 1999

Keywords

• nonn

Comments

The minimal 2^n - Germain primes in order of increasing exponent n.

Examples

			The 10th term is 13, the first term in 1024-Germain prime sequence: {13,19,37,79,223,...}. The largest prime was found for 2^79: both 1427 and 604462909807314587353088*1427 + 1 = 862568572295037916152856577 are primes.
		

Links

• Joerg Arndt, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A051686, A005384, A023212, A023228, A051887, A051888, A051900.

Programs

Mathematica

Table[p = 2; While[! PrimeQ[2^n*p + 1], p = NextPrime@ p]; p, {n, 0, 71}] (* Michael De Vlieger, Mar 05 2017 *)

PARI

P=10^6;
default(primelimit,P);
a(n)={my(N=2^n);forprime(p=2,P,if(isprime(N*p+1),return(p)));}
vector(66,n,a(n))
/* Joerg Arndt, Jun 18 2012 */

Formula

a(n) = (A051900(n)-1)/2^n. - Amiram Eldar, Feb 28 2025

Extensions

Better name by Joerg Arndt, Jun 18 2012