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%I #8 Jun 24 2015 04:21:45
%S 1365,3045,4305,4485,4785,4845,5005,5313,6045,6405,7161,7665,8265,
%T 8745,9165,9345,9933,10005,10101,10465,10545,10605,10965,11305,11685,
%U 12441,12597,13585,14385,14421,14973,15045,15405,15645,15873,16185,16485,17085,17385
%N Products p*q*r*s of distinct primes for which (p*q*r*s + 1)/2 is prime.
%e 1365 = 3*5*7*13, and (1365+1)/2 = 683, a prime.
%t t = Select[Range[1, 20000, 2], Map[Last, FactorInteger[#]] == Table[1, {4}] &]; Take[(t + 1)/2, 120] (* A234500*)
%t v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A234501 *)
%t (w + 1)/2 (* A234502 *) (* _Peter J. C. Moses_, Dec 23 2013 *)
%Y Cf. A234500, A234502, A234498, A234103.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jan 01 2014