A325957 Sophie Germain primes equal to the sum of the first k Sophie Germain primes for some k.

2, 5, 39233, 50969, 5402909, 6899969, 7722119, 10490933, 24296873, 46322183, 95837639, 117933353, 122693729, 132514703, 181862003, 303953873, 762321281, 929234279, 1044329843, 1150361501, 1335588539, 1353590321, 1662019811, 2048876033, 2176318433, 2250982931

Offset: 1

Author

Metin Sariyar, Sep 10 2019

Keywords

• nonn

Comments

The sum of first 268 terms of this sequence is also a Sophie Germain prime. 2 + 5 + 39233 + ... + 1187321288921 = 91753770231881.

Examples

			39233 is a term because sum of the first 56 Sophie Germain primes 2 + 3 + 5 + ... + 1811 = 39233 is prime and 39233*2+1 = 78467 is prime.
		

Links

• Metin Sariyar, Table of n, a(n) for n = 1..999

Crossrefs

Cf. A000040, A005384, A005385, A013918, A066819, A172037.

Programs

Mathematica

lst={}; s=0; Do[If[PrimeQ[n]&&PrimeQ[2*n+1], s=s+n; If[PrimeQ[s]&&PrimeQ[s*2+1], AppendTo[lst, s]]], {n, 1, 1000000}]; lst

PARI

issg(p) = isprime(2*p+1);
lista(nn) = {my(s=0); forprime(p=2, nn, if (issg(p), s + = p; if (isprime(s) && issg(s), print1(s, ", "); ); ); ); } \\ Michel Marcus, Sep 11 2019

Formula

Equals A005384 Intersection A066819.