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

Author

Jonathan Vos Post, Jan 23 2010

Keywords

• easy
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

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}.}.

Extensions

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