A233562 Products p*q of distinct primes such that (p*q + 1)/2 is a prime.

21, 33, 57, 85, 93, 133, 141, 145, 177, 201, 205, 213, 217, 253, 301, 381, 393, 445, 453, 481, 501, 537, 553, 565, 633, 697, 717, 745, 793, 817, 865, 913, 921, 933, 973, 1041, 1081, 1137, 1141, 1261, 1285, 1293, 1317, 1345, 1401, 1417, 1437, 1465, 1477, 1501

Offset: 1

Author

Clark Kimberling, Dec 14 2013

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Crossrefs

Cf. A233561, A046388.

Cf. A128283.

Programs

Mathematica

t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t + 1)/2, 120] (* A234096 *)
v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A233562 *)
(w + 1)/2 (* A234098 *)    (* Peter J. C. Moses, Dec 23 2013 *)
With[{nn=50},Take[Union[Select[Times@@@Subsets[Prime[Range[2nn]],{2}], PrimeQ[ (#+1)/2]&]],nn]] (* Harvey P. Dale, Mar 24 2015 *)