A165635 Primes of the form (p^2 - 3)/2 where p is also prime.

3, 11, 23, 59, 83, 179, 263, 419, 479, 683, 839, 1103, 2243, 2663, 3119, 4703, 5099, 5303, 5939, 11399, 12323, 19403, 22259, 25763, 27143, 28559, 33023, 34583, 42923, 47123, 54779, 56783, 60899, 62303, 64439, 67343, 75659, 78803, 83639, 98123

Offset: 1

Author

Vincenzo Librandi, Sep 23 2009

Keywords

• nonn
• easy

Comments

The sequence could be generated by searching for squared primes p^2 in A153238.

Examples

			The prime 3=(3^2-3)/2 is generated by p=3. The prime 11=(5^2-3)/2 is generated by p=5. The prime 23 by p=7.
		

Links

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

Crossrefs

Cf. A110589, A153238.

Programs

Magma

[a: p in PrimesInInterval(1, 500) | IsPrime(a) where a is (p^2 - 3) div 2]; // Vincenzo Librandi, Oct 12 2012

Mathematica

Select[Table[(p^2 - 3)/2, {p, Prime[Range[300]]}], PrimeQ] (* Vincenzo Librandi, Oct 12 2012 *)

Formula

a(n) = (A110589(n)^2-3)/2 .

Extensions

More terms from Max Alekseyev, Sep 25 2009

Comment clarified by R. J. Mathar, Oct 07 2009