OFFSET
1,1
COMMENTS
Define a generalized Sophie Germain n-prime of degree m, p, to be an n-prime (n-almost prime) such that 2p+1 is an m-prime (m-almost prime). For example, p=24 is a Sophie Germain 4-prime of degree 2 because 24 is a 4-prime and 2*24+1=49 is a 2-prime. Then this sequence gives all the Sophie Germain 2-primes of degree 2.
LINKS
Marius A. Burtea, Table of n, a(n) for n = 1..7675 (first 1000 terms from T. D. Noe)
FORMULA
a(n) = (A176896(n) - 1)/2. - Zak Seidov, Sep 10 2012
EXAMPLE
a(4)=34 because 34 is the 4th semiprime such that 2*34+1=69 is also a semiprime.
MATHEMATICA
SemiPrimeQ[n_] := (Plus@@Transpose[FactorInteger[n]][[2]]==2); Select[Range[2, 500], SemiPrimeQ[ # ]&&SemiPrimeQ[2#+1]&] (* T. D. Noe, Oct 20 2005 *)
fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Range[445], fQ[ # ] && fQ[2# + 1] &] (* Robert G. Wilson v, Oct 20 2005 *)
Flatten@Position[PrimeOmega@{#, 1+2*#}&/@Range@1000, {2, 2}] (* Hans Rudolf Widmer, Nov 25 2023 *)
PROG
(Magma) f:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [4..500] | f(n) and f(2*n+1)]; // Marius A. Burtea, Jan 04 2019
(PARI) isok(n) = (bigomega(n) == 2) && (bigomega(2*n+1) == 2); \\ Michel Marcus, Jan 04 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Oct 19 2005
EXTENSIONS
STATUS
approved