A056905 Primes of the form k^2 + 5.

5, 41, 149, 1301, 2309, 5189, 6089, 9221, 13001, 15881, 26249, 28229, 39209, 41621, 60521, 66569, 86441, 112901, 116969, 138389, 171401, 186629, 207941, 213449, 242069, 254021, 266261, 285161, 304709, 331781, 345749, 352841, 389381, 443561

Offset: 1

Author

Henry Bottomley, Jul 07 2000

Keywords

• nonn
• easy

Comments

Except for a(0), a(n) mod 180 = 41 or 149 since k must be a multiple of 6 without being a multiple of 30 for k^2+5 to be prime.

Examples

			a(2)=149 since 12^2 + 5 = 149, which is prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1800
• Eric Weisstein's World of Mathematics, Near-Square Prime

Crossrefs

Cf. A002496, A056899, A049423, A005473.

Programs

Magma

[a: n in [0..700] | IsPrime(a) where a is n^2+5]; // Vincenzo Librandi, Nov 30 2011

Mathematica

Select[Table[n^2+5,{n,0,7000}],PrimeQ] (* Vincenzo Librandi, Nov 30 2011 *)

PARI

is(n) = ispseudoprime(n) && issquare(n-5) \\ Felix Fröhlich, May 25 2018

Formula

a(n) = 36 * A056906(n) + 5.