A165352 Primes of the form p + (p^2 - 1)/8, where p is also prime.

13, 53, 89, 151, 251, 701, 739, 859, 1429, 1709, 2143, 3001, 4751, 7019, 8513, 10151, 12401, 14533, 17203, 18719, 21319, 23869, 27259, 30133, 41039, 42193, 44549, 45751, 46663, 52973, 82619, 99233, 104651, 114479, 120293, 135979, 138599, 148783, 151523

Offset: 1

Author

Vincenzo Librandi, Sep 16 2009

Keywords

• nonn
• easy

Comments

Primes of the form k+(k^2-1)/8, where k >0 are prime or composite, are the superset 13, 19, 43, 53, 89, 103 etc.

Links

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

Crossrefs

Cf. A165353, A165354.

Programs

Magma

[a: p in PrimesInInterval(3, 1200) | IsPrime(a) where a is p + (p^2 - 1) div 8 ]; // Vincenzo Librandi, Oct 12 2012

Mathematica

Select[Table[p + (p^2 - 1)/8, {p, Prime[Range[200]]}], PrimeQ] (* Vincenzo Librandi, Oct 12 2012 *)

PARI

forprime(p=3,1e4,if(isprime(t=p^2>>3+p),print1(t", "))) \\ Charles R Greathouse IV, May 15 2013

Formula

a(n) = A165353(n)+(A165353(n)^2-1)/8.

Extensions

More terms from R. J. Mathar, Sep 21 2009