Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Jul 23 2023 01:52:48
%S 195,255,399,455,483,555,615,627,663,759,795,915,935,1095,1235,1239,
%T 1295,1419,1455,1479,1515,1547,1595,1659,1767,1955,2067,2139,2235,
%U 2247,2343,2387,2555,2595,2607,2639,2847,2895,2919,2967,3219,3243,3335,3395,3399
%N Products p*q*r of distinct primes for which (p*q*r - 1)/2 is prime.
%H Harvey P. Dale, <a href="/A234100/b234100.txt">Table of n, a(n) for n = 1..274</a> (all terms up to 20000)
%e 97 = (3*5*13 - 1)/2, and 3*5*13 is the least product p*q*r of 3 distinct primes for which (p*q*r - 1)/2 is prime, so a(1) = 3*5*13.
%t t = Select[Range[1, 10000, 2], Map[Last, FactorInteger[#]] == Table[1, {3}] &]; Take[(t - 1)/2, 120] (* A234099 *)
%t v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* this sequence *)
%t (w - 1)/2 (* A234101 *) (* _Peter J. C. Moses_, Dec 23 2013 *)
%t With[{upto=4000},Select[Union[Times@@@Select[Subsets[Prime[ Range[ PrimePi[ upto/ 6]]],{3}],PrimeQ[(Times@@#-1)/2]&]],#<=upto&]] (* _Harvey P. Dale_, May 12 2017 *)
%Y Cf. A234099, A234101, A234093, A234102.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Dec 27 2013