A056908 Numbers k such that 36*k^2 + 36*k + 13 is prime.

0, 2, 4, 5, 7, 9, 14, 19, 22, 24, 29, 30, 34, 40, 42, 44, 50, 59, 62, 70, 72, 74, 75, 79, 80, 82, 84, 95, 102, 110, 119, 125, 132, 135, 139, 149, 150, 157, 160, 165, 172, 180, 197, 199, 200, 209, 210, 212, 224, 225, 227, 229, 230, 232, 235, 240, 244, 249

Offset: 1

Author

Henry Bottomley, Jul 07 2000

Keywords

• nonn
• easy

Comments

36*k^2 + 36*k + 13 = (6*k+3)^2 + 4, which is 4 more than a square.

Examples

			a(2)=4 since 36*4^2 + 36*4 + 13 = 733, which is prime (as well as being four more than a square).
		

Links

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

Crossrefs

This sequence and formula, together with A056907 and its formula, generate all primes of the form k^2+4, i.e., A005473.

Cf. A056900, A056902, A056904, A056906.

Programs

Magma

[n: n in [0..70]| IsPrime(36*n^2+36*n+13)]; // Vincenzo Librandi, Jul 14 2012

Mathematica

Select[Range[0,700],PrimeQ[36#^2+36#+13]&] (* Vincenzo Librandi, Jul 14 2012 *)

PARI

is(n)=isprime(36*n^2+36*n+13) \\ Charles R Greathouse IV, Mar 01 2017