A145472 Primes p such that (p+7)/2 is prime.

3, 7, 19, 31, 67, 79, 127, 139, 151, 199, 211, 271, 307, 379, 439, 547, 607, 619, 691, 727, 739, 751, 787, 811, 859, 907, 919, 967, 991, 1039, 1087, 1231, 1279, 1447, 1459, 1471, 1531, 1567, 1699, 1747, 1759, 1831, 1867, 1987, 2011, 2131, 2179, 2239, 2251

Offset: 1

Author

Artur Jasinski, Oct 11 2008

Keywords

• nonn
• easy

Comments

All these primes are congruent to 3 mod 4 and (with the exception of the first one) to 7 mod 12.

Links

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

Crossrefs

Cf. A092109, A145471-A145480, A063910.

Programs

Magma

[p: p in PrimesUpTo(2500)| IsPrime((p + 7) div 2)]; // Vincenzo Librandi, Feb 04 2013

Mathematica

aa = {}; k = 7; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(#+7)/2]&] (* Harvey P. Dale, Jan 11 2020 *)

PARI

list(n)=my(t=1, p, i=1); while(i2&&isprime((7+p)/2), print1(n, ", "))) \\Anders Hellström, Jan 23 2017

PARI

list(lim)=my(v=List()); forprime(p=3,lim, if(isprime((p+7)/2), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017