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
KEYWORD
nonn
AUTHOR
Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Oct 24 2005
EXTENSIONS
Extended by Ray Chandler, Oct 31 2005
STATUS
approved