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 A234104 #12 Jan 29 2023 14:56:28
%S A234104 53,83,137,173,179,193,233,281,353,389,431,443,449,479,503,523,557,
%T A234104 587,593,641,677,773,823,827,839,853,953,983,1019,1033,1061,1093,1097,
%U A234104 1117,1151,1187,1223,1277,1307,1433,1439,1453,1493,1511,1579,1583,1601,1619
%N A234104 Primes of the form (p*q*r + 1)/2, where p, q, r are distinct primes.
%H A234104 Robert Israel, <a href="/A234104/b234104.txt">Table of n, a(n) for n = 1..10000</a>
%e A234104 (3*5*7 + 1)/2 = 53.
%p A234104 filter:= proc(n) local s;
%p A234104 if not isprime(n) then return false fi;
%p A234104 s:= ifactors(2*n-1)[2];
%p A234104 nops(s)=3 and map(t -> t[2],s)=[1,1,1]
%p A234104 end proc:
%p A234104 select(filter, [seq(i,i=3..1619,2)]); # _Robert Israel_, May 11 2020
%t A234104 t = Select[Range[1, 10000, 2], Map[Last, FactorInteger[#]] == Table[1, {3}] &]; Take[(t + 1)/2, 120] (* A234102 *)
%t A234104 v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A234103 *)
%t A234104 (w + 1)/2 (* A234104 *) (* _Peter J. C. Moses_, Dec 23 2013 *)
%t A234104 Module[{nn=100},Select[(Times@@#+1)/2&/@Subsets[Prime[Range[nn]],{3}],PrimeQ[ #] && #<=5*Prime[nn]&]]//Union (* _Harvey P. Dale_, Jan 29 2023 *)
%Y A234104 Cf. A234102, A234103, A234101.
%K A234104 nonn,easy
%O A234104 1,1
%A A234104 _Clark Kimberling_, Dec 27 2013