This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A233562 #15 Nov 01 2020 01:38:53
%S A233562 21,33,57,85,93,133,141,145,177,201,205,213,217,253,301,381,393,445,
%T A233562 453,481,501,537,553,565,633,697,717,745,793,817,865,913,921,933,973,
%U A233562 1041,1081,1137,1141,1261,1285,1293,1317,1345,1401,1417,1437,1465,1477,1501
%N A233562 Products p*q of distinct primes such that (p*q + 1)/2 is a prime.
%C A233562 This sequence is a subsequence of A128283 since the condition that (p+q)/2 be prime is not required here. The smallest number not in A128283 is 141=3*47 since (3+47)/2=25. - _Hartmut F. W. Hoft_, Oct 31 2020
%e A233562 21 = 3*7 is the least product of distinct primes p and q for which (p*q + 1)/2 is a prime, so a(1) = 21.
%t A233562 t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t + 1)/2, 120] (* A234096 *)
%t A233562 v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A233562 *)
%t A233562 (w + 1)/2 (* A234098 *) (* _Peter J. C. Moses_, Dec 23 2013 *)
%t A233562 With[{nn=50},Take[Union[Select[Times@@@Subsets[Prime[Range[2nn]],{2}], PrimeQ[ (#+1)/2]&]],nn]] (* _Harvey P. Dale_, Mar 24 2015 *)
%Y A233562 Cf. A233561, A046388.
%Y A233562 Cf. A128283.
%K A233562 nonn,easy
%O A233562 1,1
%A A233562 _Clark Kimberling_, Dec 14 2013