A056906 Numbers k such that 36*k^2 + 5 is prime.

0, 1, 2, 6, 8, 12, 13, 16, 19, 21, 27, 28, 33, 34, 41, 43, 49, 56, 57, 62, 69, 72, 76, 77, 82, 84, 86, 89, 92, 96, 98, 99, 104, 111, 119, 121, 126, 128, 131, 132, 133, 134, 139, 142, 146, 148, 153, 159, 166, 168, 169, 173, 174

Offset: 1

Author

Henry Bottomley, Jul 07 2000

Keywords

• nonn
• easy

Comments

Except for a(1), a(n) is never a multiple of 5.

Examples

			a(3)=2 since 36*2^2 + 5 = 149, which is prime.
		

Links

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

Crossrefs

This sequence and formula generate all primes of the form k^2+5, i.e., A056905.

Except for the first term, this sequence is a subsequence of A047201.

Cf. A056900, A056902.

Programs

Magma

[n: n in [0..200]| IsPrime(36*n^2+5)]; // Vincenzo Librandi, Jul 14 2012

Mathematica

Select[Range[0,200],PrimeQ[36#^2+5]&] (* Harvey P. Dale, Jul 25 2011 *)

PARI

is(n)=isprime(36*n^2+5) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = sqrt(A056905(n)-5)/6.

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 09 2011