A234096 Integers of the form (p*q + 1)/2, where p and q are distinct primes.

8, 11, 17, 18, 20, 26, 28, 29, 33, 35, 39, 43, 44, 46, 47, 48, 56, 58, 60, 62, 65, 67, 71, 72, 73, 78, 80, 81, 89, 92, 93, 94, 101, 102, 103, 105, 107, 108, 109, 110, 111, 118, 119, 124, 125, 127, 130, 133, 134, 144, 146, 148, 150, 151, 152, 153, 155, 160

Offset: 1

Author

Clark Kimberling, Dec 27 2013

Keywords

• nonn
• easy

Examples

			(3*5 + 1)/2 = 8, (3*7 + 1)/2 = 11.
		

Crossrefs

Cf. A234093, A233562, A234098.

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 *)

Formula

1 + A234093.