A234093 Integers of the form (p*q - 1)/2, where p and q are distinct primes.

7, 10, 16, 17, 19, 25, 27, 28, 32, 34, 38, 42, 43, 45, 46, 47, 55, 57, 59, 61, 64, 66, 70, 71, 72, 77, 79, 80, 88, 91, 92, 93, 100, 101, 102, 104, 106, 107, 108, 109, 110, 117, 118, 123, 124, 126, 129, 132, 133, 143, 145, 147, 149, 150, 151, 152, 154, 159

Offset: 1

Author

Clark Kimberling, Dec 27 2013

Keywords

• nonn
• easy

Comments

A102770 is subsequence. - Zak Seidov, Feb 21 2014

Examples

			(3*5 - 1)/2 = 7; (3*7 - 1)/2 = 10.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A102770, A233561, A234095, A234096.

Programs

Mathematica

t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t - 1)/2, 120] (* A234093 *)
v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A233561 *)
(w - 1)/2 (* A234095 *) (* Peter J. C. Moses, Dec 23 2013 *)
With[{nn=60},Take[Union[Select[(Times@@#-1)/2&/@Subsets[Prime[ Range[ nn]],{2}],IntegerQ]],nn]] (* Harvey P. Dale, Mar 08 2015 *)