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%I #22 Sep 24 2015 12:13:55
%S 15,51,85,91,133,145,235,249,265,427,451,493,519,559,565,589,591,681,
%T 721,871,879,1003,1149,1177,1189,1207,1411,1441,1509,1561,1603,1651,
%U 1837,1945,2059,2071,2119,2227,2335,2391,2419,2599,2661,2827,2869,2965,2995
%N Semiprimes n = p*q, p<q, such that both numbers n + p - 1 and n + q - 1 are prime.
%C Subsequence of A006881.
%H Peter J. C. Moses, <a href="/A227129/b227129.txt">Table of n, a(n) for n = 1..5000</a>
%H Since 591 = 3*197 and numbers 591 + 3 - 1 = 593, 591 + 197 - 1 = 787 are both primes, then 591 is in the sequence.
%F A226770(a(n)-1) = 2.
%t Select[Range[10000],(Last[#2]=={1,1}&&And@@PrimeQ[#1+First[#2]-1]&)[#1,Transpose[FactorInteger[#1]]]&] (* _Peter J. C. Moses_, Jul 03 2013 *)
%t spQ[n_]:=Module[{fi=Transpose[FactorInteger[n]]},fi[[2]]=={1,1}&&AllTrue[ n-1+fi[[1]],PrimeQ]]; Select[Range[3000],spQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 24 2015 *)
%Y Cf. A006881, A226770.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Jul 02 2013
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