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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A111153, A001358, A005384, A111207.

Sequence in context: A122492 A178378 A133234 * A087112 A077554 A262812

Adjacent sequences: A111203 A111204 A111205 * A111207 A111208 A111209

Keyword

nonn

Author

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

Extensions

Extended by Ray Chandler, Oct 31 2005

Status

approved