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 A234500 #10 Oct 18 2021 15:41:58
%S A234500 578,683,893,998,1073,1208,1403,1502,1523,1568,1628,1658,1853,1898,
%T A234500 1943,1964,2153,2195,2243,2258,2321,2393,2423,2468,2503,2558,2594,
%U A234500 2657,2783,2828,2933,3023,3053,3098,3140,3203,3273,3278,3350,3383,3392,3518,3548,3581
%N A234500 Integers of the form (p*q*r*s + 1)/2, where p, q, r, s are distinct primes.
%F A234500 1 + A234105.
%e A234500 578 = (3*5*7*11 + 1)/2.
%t A234500 t = Select[Range[1, 20000, 2], Map[Last, FactorInteger[#]] == Table[1, {4}] &]; Take[(t + 1)/2, 120] (* A234500*)
%t A234500 v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A234501 *)
%t A234500 (w + 1)/2 (* A234502 *) (* _Peter J. C. Moses_, Dec 23 2013 *)
%t A234500 With[{nn=20},Select[Union[(Times@@#+1)/2&/@Subsets[Prime[Range[2,nn]],{4}]],#<=(105Prime[nn]+1)/2&]] (* _Harvey P. Dale_, Oct 18 2021 *)
%Y A234500 Cf. A234099, A234103, A234104.
%K A234500 nonn,easy
%O A234500 1,1
%A A234500 _Clark Kimberling_, Jan 01 2014