A145476 Primes p such that (19 + p)/2 is prime.

3, 7, 19, 43, 67, 103, 127, 139, 199, 283, 307, 367, 379, 439, 463, 523, 547, 607, 643, 727, 739, 823, 859, 907, 1063, 1123, 1303, 1327, 1399, 1447, 1459, 1483, 1627, 1699, 1747, 1999, 2083, 2239, 2287, 2383, 2539, 2887, 3067, 3079, 3307, 3319, 3463, 3499

Offset: 1

Author

Artur Jasinski, Oct 11 2008

Keywords

• nonn

Comments

All these primes are congruent to 3 mod 4 and (with the exception of the first term) to 5 mod 12.

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A092109, A145471-A145480.

Programs

Mathematica

aa = {}; k = 19; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(#+19)/2]&] (* Harvey P. Dale, Sep 06 2023 *)

PARI

list(n)=my(t=1,p,i=1);while(i2&&bigomega((19+p)/2)==1,print(p))) \\ Anders Hellström, Jan 22 2017