A007591 Numbers k such that k^2 + 4 is prime.

1, 3, 5, 7, 13, 15, 17, 27, 33, 35, 37, 45, 47, 57, 65, 67, 73, 85, 87, 95, 97, 103, 115, 117, 125, 135, 137, 147, 155, 163, 167, 177, 183, 193, 203, 207, 215, 217, 233, 235, 243, 245, 253, 255, 265, 267, 275, 277, 287, 293, 303, 307, 313, 317, 347, 357, 373, 375

Offset: 1

Author

N. J. A. Sloane, R. K. Guy

Keywords

• nonn
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, 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), A049422 (i=3), this sequence (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

Magma

[n: n in [0..400] | IsPrime(n^2+4)]; // Vincenzo Librandi, Nov 18 2010

Mathematica

lst={};Do[If[PrimeQ[n^2+4], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)
Select[Range[0, 400], PrimeQ[#^2 + 4] &] (* Vincenzo Librandi, Sep 25 2012 *)

PARI

select(n->isprime(n^2+4),vector(500,n,2*n-1)) \\ Charles R Greathouse IV, Sep 25 2012