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%I #15 Nov 02 2017 17:48:51
%S 15,35,39,87,95,119,123,143,159,203,215,219,299,303,327,335,395,447,
%T 515,527,543,623,635,695,699,707,767,779,803,843,879,899,923,959,1007,
%U 1043,1047,1115,1139,1199,1203,1227,1263,1347,1355,1383,1403,1623,1643
%N Products p*q of distinct primes such that (p*q - 1)/2 is prime.
%H Harvey P. Dale, <a href="/A233561/b233561.txt">Table of n, a(n) for n = 1..1000</a>
%e 15 = 3*5 is the least product of distinct primes p and q for which (p*q - 1)/2 is prime, so a(1) = 15.
%t t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t - 1)/2, 120] (* A234093 *)
%t v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A233561 *)
%t (w - 1)/2 (* A234095 *) (* _Peter J. C. Moses_, Dec 23 2013 *)
%t With[{upto=2000},Select[Times@@#&/@Select[Subsets[Prime[Range[ PrimePi[ upto/2]]],{2}],PrimeQ[(Times@@#-1)/2]&]//Union,#<=upto&]] (* _Harvey P. Dale_, Nov 02 2017 *)
%Y Cf. A234093, A234095, A046388.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Dec 14 2013
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