A007591 Numbers k such that k^2 + 4 is prime. (Formerly M2416)

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

1,2

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

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 *)

Prog

(Magma) [n: n in [0..400] | IsPrime(n^2+4)]; // Vincenzo Librandi, Nov 18 2010
(PARI) select(n->isprime(n^2+4), vector(500, n, 2*n-1)) \\ Charles R Greathouse IV, Sep 25 2012

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).

Sequence in context: A285130 A024909 A063241 * A097687 A032911 A157834

Adjacent sequences: A007588 A007589 A007590 * A007592 A007593 A007594

Keyword

nonn,easy

Author

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

Status

approved