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 A111153 Sophie Germain semiprimes: semiprimes n such that 2n+1 is also a semiprime. 25
 4, 10, 25, 34, 38, 46, 55, 57, 77, 91, 93, 106, 118, 123, 129, 133, 143, 145, 159, 161, 169, 177, 185, 201, 203, 205, 206, 213, 218, 226, 235, 259, 267, 289, 291, 295, 298, 305, 314, 327, 334, 335, 339, 358, 361, 365, 377, 381, 394, 395, 403, 407, 415, 417 (list; graph; refs; listen; history; text; internal format)
 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. MAPLE with(numtheory): P:=proc(n) if bigomega(n)=2 and bigomega(2*n+1)=2 then n; fi; end: seq(P(i), i=1..10^4); # Paolo P. Lava, Mar 10 2017 MATHEMATICA SemiPrimeQ[n_] := (Plus@@Transpose[FactorInteger[n]][]==2); Select[Range[2, 500], SemiPrimeQ[ # ]&&SemiPrimeQ[2#+1]&] (* T. D. Noe, Oct 20 2005 *) fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Range, fQ[ # ] && fQ[2# + 1] &] (* Robert G. Wilson v, Oct 20 2005 *) PROG (MAGMA) f:=func< n | &+[k: 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 Cf. A005384, A001358, A111168, A111170, A111171, A111173, A111176, A176896. Sequence in context: A127070 A107961 A051864 * A265438 A145368 A266826 Adjacent sequences:  A111150 A111151 A111152 * A111154 A111155 A111156 KEYWORD nonn AUTHOR Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Oct 19 2005 EXTENSIONS Corrected and extended by T. D. Noe, Ray Chandler and Robert G. Wilson v, Oct 20 2005 STATUS approved

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Last modified February 21 22:10 EST 2020. Contains 332113 sequences. (Running on oeis4.)