A234098 Primes of the form (p*q + 1)/2, where p and q are distinct primes.

11, 17, 29, 43, 47, 67, 71, 73, 89, 101, 103, 107, 109, 127, 151, 191, 197, 223, 227, 241, 251, 269, 277, 283, 317, 349, 359, 373, 397, 409, 433, 457, 461, 467, 487, 521, 541, 569, 571, 631, 643, 647, 659, 673, 701, 709, 719, 733, 739, 751, 757, 769, 821

Offset: 1

Author

Clark Kimberling, Dec 27 2013

Keywords

• nonn
• easy

Examples

			11 = (3*7 + 1)/2, 17 = (5*7 + 1)/2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A234096, A233562, A234095.

Cf. A010051, A046388.

Programs

Haskell

a234098 n = a234098_list !! (n-1)
a234098_list = filter ((== 1) . a010051') $
                      map ((flip div 2) . (+ 1)) a046388_list
-- Reinhard Zumkeller, Jan 02 2014

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 *)
Take[Select[(Times@@#+1)/2&/@Subsets[Prime[Range[200]],{2}],PrimeQ]//Union,60] (* Harvey P. Dale, Jun 24 2025 *)