A157342 - OEIS

%I #16 Feb 12 2022 09:36:16

%S 49,91,119,133,169,217,221,247,259,289,301,323,329,361,403,413,427,

%T 469,481,497,511,527,553,559,589,611,629,679,703,707,721,731,749,763,

%U 767,793,799,817,871,889,893,923,949,959,961,973,1003,1027,1037,1043,1057

%N Semiprimes that are the product of two non-Sophie Germain primes.

%H G. C. Greubel, <a href="/A157342/b157342.txt">Table of n, a(n) for n = 1..5000</a>

%e 49 = 7*7, 2*7 + 1 = 15 (not prime);

%e 91 = 7*13, 2*7 + 1 = 15 (not prime), 2*13 + 1 = 27 (not prime); ...

%t 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

%t With[{nn=60},Take[Times@@@Tuples[Select[Prime[Range[nn]],!PrimeQ[ 2#+1]&], 2] // Union,nn]] (* _Harvey P. Dale_, Feb 15 2017 *)

%Y Cf. A001358, A005384, A111206.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 27 2009