A111206 Semi-Sophie Germain semiprimes: semiprimes which are the product of Sophie Germain primes.

4, 6, 9, 10, 15, 22, 25, 33, 46, 55, 58, 69, 82, 87, 106, 115, 121, 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, 529, 537, 562, 565, 573, 583, 586, 655, 667, 699, 717, 718, 753, 838

Offset: 1

Author

Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Oct 24 2005

Keywords

• nonn

Comments

Define an n-almost Sophie Germain almost-prime to be an n-almost prime all the prime factors of which are Sophie Germain primes. Note the contrast between this terminology and that of Sophie Germain n-almost primes, they are different.

Examples

			a(4) = 10 because 10 is the 4th semiprime both the prime factors of which are Sophie Germain primes.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A111153, A001358, A005384, A111207.

Programs

Mathematica

lst={};Do[If[Plus@@Last/@FactorInteger[n]==2,a=First/@FactorInteger[n];b=a[[1]];k=0;If[Length[a]==2,c=a[[2]];If[ !PrimeQ[2*c+1],k=1]];If[PrimeQ[2*b+1]&&k==0,AppendTo[lst,n]]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 27 2009 *)
Module[{nn=100,sgp},sgp=Select[Prime[Range[100]],PrimeQ[2#+1]&];Select[ Union[ Times@@@Tuples[sgp,2]],#<=10nn&]] (* Harvey P. Dale, May 08 2019 *)

PARI

list(lim)=my(v=List(),u=v,t); forprime(p=2,lim\2, if(isprime(2*p+1), listput(u,p))); for(i=1,#u, for(j=1,i, t=u[i]*u[j]; if(t>lim, break); listput(v,t))); Set(v) \\ Charles R Greathouse IV, Feb 05 2017

Extensions

Extended by Ray Chandler, Oct 31 2005