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

1,1

Comments

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

Links

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

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}.}.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A007506 A042693 A328746 * A301993 A128297 A183291

Adjacent sequences: A172034 A172035 A172036 * A172038 A172039 A172040

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 23 2010

Extensions

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

Status

approved