A088502 Numbers n such that (n^2 - 5)/4 is prime.

5, 7, 9, 11, 13, 17, 19, 21, 23, 27, 31, 33, 39, 41, 43, 49, 53, 57, 61, 63, 71, 77, 79, 83, 89, 91, 93, 97, 101, 107, 109, 111, 113, 119, 121, 129, 131, 133, 137, 141, 153, 167, 171, 173, 179, 187, 189, 193, 201, 203, 207, 229, 231, 241, 251, 253, 261, 263, 269

Offset: 1

Author

Pierre CAMI, Nov 13 2003

Keywords

• easy
• nonn

Comments

Under Bunyakovsky's conjecture this sequence is infinite. - Charles R Greathouse IV, Dec 28 2011

Examples

			(23*23 - 5)/4 = 131, 131 is prime, 23 is the 9th n of the sequence.
		

Links

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

Crossrefs

Cf. A002327, A002328, A110013.

Programs

Magma

[n: n in [1..300 by 2] | IsPrime((n^2-5) div 4)]; // Vincenzo Librandi, Oct 06 2012

Mathematica

Select[Range[500], PrimeQ[(#^2 - 5)/4] &] (* Vincenzo Librandi, Oct 06 2012 *)

PARI

for(k=2,1e3,if(isprime(k^2+k-1),print1(2*k+1", "))) \\ Charles R Greathouse IV, Dec 28 2011

Formula

a(n) = 2*A002328(n) - 1 = Sqrt(A110013(n)). - Ray Chandler, Sep 07 2005