A145471 Primes p such that (5+p)/2 is prime.

5, 17, 29, 41, 53, 89, 101, 113, 137, 173, 197, 257, 269, 293, 353, 389, 449, 461, 509, 521, 557, 617, 701, 761, 773, 797, 857, 881, 929, 953, 977, 1013, 1109, 1181, 1193, 1229, 1277, 1289, 1301, 1361, 1433, 1481, 1613, 1637, 1709, 1721, 1877, 1889, 1901

Offset: 1

Author

Artur Jasinski, Oct 11 2008

Keywords

• nonn

Comments

All these primes are congruent to 1 mod 4 and to 5 mod 12.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A063909, A092109.

Subsequence of A040117. - Zak Seidov, Feb 21 2016

Programs

Magma

[p: p in PrimesInInterval(3,2000) | IsPrime((5+p) div 2)]; // Vincenzo Librandi, Feb 25 2016

Maple

select(t -> isprime(t) and isprime((t+5)/2), [seq(i, i=5..1000, 12)]); # Robert Israel, Feb 24 2016

Mathematica

aa = {}; k = 5; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(5+#)/2]&]  (* Harvey P. Dale, Apr 23 2011 *)

PARI

forprime(p=2,1e4,if(p%12!=5,next);if(isprime(p\2+3),print1(p", "))) \\ Charles R Greathouse IV, Jul 16 2011

Formula

a(n) = 2*A063909(n)-5. - Robert Israel, Feb 24 2016