A163634 a(n) = (p*(p+4)+1)/2 where (p,p+4) are the n-th cousin prime pair.

11, 39, 111, 219, 759, 1011, 2379, 3279, 4899, 5511, 6159, 8319, 13611, 19011, 25311, 26679, 38919, 47739, 49611, 61599, 72579, 79599, 97239, 105339, 108111, 119559, 125499, 189111, 208011, 227811, 274539, 288039, 297219, 340311, 365511, 370659

Offset: 1

Author

Vincenzo Librandi, Aug 02 2009

Keywords

• nonn

Examples

			a(1) =  (3* 7 + 1)/2 =  11;
a(2) =  (7*11 + 1)/2 =  39;
a(3) = (13*17 + 1)/2 = 111.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..112

Crossrefs

Cf. A023200, A046132.

Programs

Magma

[(p*(p+4)+1)/2: p in PrimesUpTo(1000)| IsPrime(p+4)]; // Vincenzo Librandi, May 17 2014

Mathematica

(fQ[n_]:=Block[{fi=FactorInteger@n}, Last@#&/@fi=={1, 1}&&Differences[First@#&/@fi]=={4}]; Select[Range@8000000, fQ] + 1)/2 (* Vincenzo Librandi Jan 02 2018 *)
Join[{11},(1+Times@@#)/2&/@Select[Partition[Prime[Range[250]],2,1],#[[2]]- #[[1]]==4&]] (* Harvey P. Dale, Apr 04 2022 *)

Formula

a(n) = (A143206(n) + 1)/2.

Extensions

Entries checked by R. J. Mathar, Aug 07 2009