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 A234103 #15 May 12 2025 18:02:05
%S A234103 105,165,273,345,357,385,465,561,705,777,861,885,897,957,1005,1045,
%T A234103 1113,1173,1185,1281,1353,1545,1645,1653,1677,1705,1905,1965,2037,
%U A234103 2065,2121,2185,2193,2233,2301,2373,2445,2553,2613,2865,2877,2905,2985,3021,3157
%N A234103 Products p*q*r of distinct primes for which (p*q*r + 1)/2 is prime.
%e A234103 105 = 3*5*7, and (105 + 1)/2 is prime.
%t A234103 t = Select[Range[1, 10000, 2], Map[Last, FactorInteger[#]] == Table[1, {3}] &]; Take[(t + 1)/2, 120] (* A234102 *)
%t A234103 v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A234103 *)
%t A234103 (w + 1)/2 (* A234104 *) (* _Peter J. C. Moses_, Dec 23 2013 *)
%t A234103 With[{nn=50},Select[Union[Select[Times@@@Subsets[Prime[Range[2,nn]],{3}],PrimeQ[(#+1)/2]&]],#<=15*Prime[nn]&]] (* _Harvey P. Dale_, May 12 2025 *)
%Y A234103 Cf. A234100, A234102, A234104.
%K A234103 nonn,easy
%O A234103 1,1
%A A234103 _Clark Kimberling_, Dec 27 2013