A117847 Numbers k such that A060256(k)*prime(k)# - 1 is a Sophie Germain prime, where prime(k)# is the k-th primorial.

1, 2, 3, 4, 8, 9, 10, 15, 24, 35, 37, 79, 340

Offset: 1

Author

Pierre CAMI, May 01 2006

Keywords

• nonn
• hard
• more

Comments

This sequence gives the firsts of twin primes (A060256(n)*prime(n)# - 1, A060256(n)*prime(n)# + 1) which are also Sophie Germain primes.

a(14) > 367. - Amiram Eldar, Sep 11 2021

Examples

			16*(29#)-1 is the first of twin primes, 16 = A060256(10), 2*(16*(29#)-1)+1 is prime so 16*(29#)-1 is a Sophie Germain prime.
		

Crossrefs

Cf. A002110, A005384, A060256.

Programs

Mathematica

q[n_] := Module[{p = Product[Prime[i], {i,1,n}], k=1}, While[!PrimeQ[k*p-1] || !PrimeQ[k*p+1], k++]; PrimeQ[2*k*p - 1]]; Select[Range[100], q] (* Amiram Eldar, Sep 11 2021 *)

Extensions

a(1)-a(6) inserted by Amiram Eldar, Sep 11 2021