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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A234096, A233562, A234095.

Cf. A010051, A046388.

Sequence in context: A330410 A111255 A060213 * A153502 A249377 A211486

Adjacent sequences: A234095 A234096 A234097 * A234099 A234100 A234101

Keyword

nonn,easy

Author

Clark Kimberling, Dec 27 2013

Status

approved