%I #71 Sep 27 2019 19:43:40

%S 2,5,39233,50969,5402909,6899969,7722119,10490933,24296873,46322183,

%T 95837639,117933353,122693729,132514703,181862003,303953873,762321281,

%U 929234279,1044329843,1150361501,1335588539,1353590321,1662019811,2048876033,2176318433,2250982931

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

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

%H Metin Sariyar, <a href="/A325957/b325957.txt">Table of n, a(n) for n = 1..999</a>

%F Equals A005384 Intersection A066819.

%e 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.

%t 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

%o (PARI) issg(p) = isprime(2*p+1);

%o 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

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

%K nonn

%O 1,1

%A _Metin Sariyar_, Sep 10 2019