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

1,1

Comments

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

Links

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

Formula

Equals A005384 Intersection A066819.

Example

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.

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

Prog

(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

Crossrefs

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

Sequence in context: A057678 A090071 A319898 * A247148 A139062 A241861

Adjacent sequences: A325954 A325955 A325956 * A325958 A325959 A325960

Keyword

nonn

Author

Metin Sariyar, Sep 10 2019

Status

approved