A088503 Numbers n such that (n^2 + 3)/4 is prime.

3, 5, 7, 11, 13, 17, 25, 29, 31, 35, 41, 43, 49, 55, 67, 77, 83, 101, 109, 115, 119, 125, 133, 139, 143, 151, 155, 157, 161, 179, 181, 199, 203, 211, 221, 223, 235, 239, 263, 277, 283, 287, 295, 301, 307, 311, 323, 325, 329, 335, 337, 347, 353, 377, 379, 385

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

			(25*25 + 3)/4 = 157, 157 is prime, 25 is the 7th term of the sequence.
		

Links

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

Crossrefs

Cf. A002383, A002384, A110284.

Programs

Magma

[n: n in [1..400 by 2] | IsPrime((n^2 + 3) div 4)]; // Vincenzo Librandi, Oct 06 2012

Mathematica

Select[Range[500], PrimeQ[(#^2 + 3)/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*A002384(n) + 1 = sqrt(A110284(n)). - Ray Chandler, Sep 07 2005

Extensions

Corrected and extended by Ray Chandler, Nov 16 2003