A175666 Sum of Sophie Germain prime p and corresponding safe prime q=2p+1.

7, 10, 16, 34, 70, 88, 124, 160, 250, 268, 340, 394, 520, 538, 574, 700, 718, 754, 844, 880, 1078, 1258, 1294, 1330, 1474, 1528, 1780, 1924, 1960, 1978, 2050, 2158, 2230, 2284, 2428, 2734, 2860, 3040, 3058, 3094, 3148, 3310, 3670, 3688, 3868, 4228, 4318

Offset

1,1

Comments

For n > 1, numbers of the form 6k-2 such that Omega( (2k-1)(4k-1) ) = 2. - Wesley Ivan Hurt, Jun 28 2013

First semiprimes: 10,34,394,538,718,1294,2734. - Zak Seidov, Sep 07 2016

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Formula

a(n) = A005384(n)+A005385(n) = 3*A005384(n)+1 = (3*A005385(n)-1)/2.

Mathematica

Total/@Select[Table[{p, 2p+1}, {p, Prime[Range[400]]}], PrimeQ[#[[2]]]&] (* Harvey P. Dale, Jan 29 2026 *)

Prog

(PARI) is(n)=n%3==1 && isprime(n\3) && isprime((2*n+1)/3) \\ Charles R Greathouse IV, Jun 28 2013

Crossrefs

Cf. A005384, A005385.

Sequence in context: A033817 A286873 A218128 * A299997 A299987 A192273

Adjacent sequences: A175663 A175664 A175665 * A175667 A175668 A175669

Keyword

nonn

Author

Zak Seidov, Aug 05 2010

Status

approved