A157344 Semiprimes that are the product of two distinct Sophie Germain primes.

6, 10, 15, 22, 33, 46, 55, 58, 69, 82, 87, 106, 115, 123, 145, 159, 166, 178, 205, 226, 249, 253, 262, 265, 267, 319, 339, 346, 358, 382, 393, 415, 445, 451, 466, 478, 502, 519, 537, 562, 565, 573, 583, 586, 655, 667, 699, 717, 718, 753, 838, 843, 862, 865

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 27 2009

Keywords

• nonn

Comments

6=2*3; 2 and 3 are Sophie Germain primes, 10=2*5; 2 and 5 are Sophie Germain primes, 15=3*5; 3 and 5 are Sophie Germain primes, ...

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001358, A005384, A111206, A157342, A006881.

Programs

Mathematica

lst={};Do[If[Plus@@Last/@FactorInteger[n]==2,a=Length[First/@FactorInteger[n]];If[a==2,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];If[PrimeQ[2*c+1]&&PrimeQ[2*d+1],AppendTo[lst,n]]]],{n,7!}];lst
nn=100;With[{sgp=Select[Prime[Range[nn]],PrimeQ[2#+1]&]},Take[ Union[ Select[ Times @@@ Subsets[sgp,{2}],PrimeOmega[#]==2&]],nn]] (* Harvey P. Dale, Nov 22 2012 *)