A049422 Numbers k such that k^2 + 3 is prime.

0, 2, 4, 8, 10, 14, 22, 28, 38, 50, 52, 62, 64, 70, 74, 76, 92, 94, 106, 112, 122, 130, 134, 140, 146, 154, 158, 160, 172, 178, 218, 230, 242, 244, 248, 256, 274, 286, 298, 304, 316, 322, 326, 340, 350, 356, 364, 368, 398, 406, 416, 424, 430, 434, 440, 458, 470

Offset: 1

Author

Paul Jobling (paul.jobling(AT)whitecross.com)

Keywords

• nonn
• easy

Examples

			4^2 + 3 = 19, which is prime.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Near-Square Prime

Crossrefs

Other sequences of the type "Numbers k such that k^2 + i is prime": A005574 (i=1), A067201 (i=2), this sequence (i=3), A007591 (i=4), A078402 (i=5), A114269 (i=6), A114270 (i=7), A114271 (i=8), A114272 (i=9), A114273 (i=10), A114274 (i=11), A114275 (i=12).

Programs

Mathematica

lst={};Do[If[PrimeQ[n^2+3], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

PARI

isA049422(n) = isprime(n^2+3) \\ Michael B. Porter, Mar 19 2010