A066819 -id:A066819 - cp's OEIS frontend

A172037 Prime partial sums of Sophie Germain primes A005384.

2, 5, 73, 167, 2423, 7621, 39233, 50969, 89563, 198139, 207029, 267143, 322963, 335117, 438517, 481207, 541547, 812051, 874697, 917611, 939293, 1077761, 1149593, 1354267, 1464011, 1695559, 1880401, 2510083, 2548703, 3115249, 3157487, 3505849, 4519057

Offset: 1

Jonathan Vos Post, Jan 23 2010

a(1) and a(2) are themselves Sophie Germain primes.

			a(1) = 2 = first Sophie Germain prime A005384(1). a(2) = 5 = sum of first two Sophie Germain primes = 2+3. a(3) = 73 = sum of first six Sophie Germain primes = 2+3+5+11+23+29.

Nathaniel Johnston, Table of n, a(n) for n = 1..1000

Cf. A000040, A005384, A005385, A066819, A172036.

Select[Accumulate[Select[Prime[Range[5000]],PrimeQ[2#+1]&]],PrimeQ] (* Harvey P. Dale, Nov 27 2013 *)

A000040 INTERSECTION A066819 = {p such that p is prime and SUM[i=1..k]A005384(k) is prime} = {p such that p is prime and SUM[i=1..k]{p is prime and 2p+1 is prime}.}.

a(7) - a(34) from Nathaniel Johnston, Apr 29 2011

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

Original entry on oeis.org

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

Metin Sariyar, Sep 10 2019

nonn

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

			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.

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

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

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

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

Equals A005384 Intersection A066819.

cp's OEIS Frontend

A172037 Prime partial sums of Sophie Germain primes A005384.

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