A028873 Numbers k such that k^2 - 3 is prime.

4, 8, 10, 14, 20, 26, 32, 34, 40, 44, 46, 58, 64, 68, 80, 86, 88, 92, 98, 110, 112, 118, 124, 128, 136, 140, 142, 146, 164, 172, 190, 194, 202, 206, 208, 218, 220, 250, 254, 266, 268, 296, 298, 304, 310, 320, 322, 326, 328, 332, 340, 350, 356, 362, 370, 416, 418

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• easy

Examples

			8^2 - 3 = 61 is prime, so 8 is in the sequence.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000
• Patrick De Geest, Palindromic Quasipronics of the form n(n+x).
• Eric Weisstein's World of Mathematics, Near-Square Prime.

Crossrefs

Cf. A028874.

Programs

Magma

[n: n in [2..10000] |IsPrime(n^2-3)]; // Vincenzo Librandi, Aug 05 2010

Mathematica

Select[Range[2, 500], PrimeQ[#^2 - 3] &] (* Amiram Eldar, Mar 01 2025 *)

PARI

is(n)=isprime(n^2-3) \\ Charles R Greathouse IV, Jul 02 2013

Formula

a(n) = sqrt(A028874(n) + 3). - Amiram Eldar, Mar 01 2025