A067201 Numbers k such that k^2 + 2 is prime.

0, 1, 3, 9, 15, 21, 33, 39, 45, 57, 81, 99, 105, 111, 117, 123, 147, 171, 219, 225, 237, 243, 249, 255, 273, 297, 303, 309, 321, 345, 351, 363, 369, 375, 387, 417, 423, 429, 441, 447, 453, 477, 501, 513, 549, 555, 561, 573, 603, 609, 651, 675, 681, 699, 711, 753

Offset: 1

Author

Benoit Cloitre, Feb 19 2002

Keywords

• nonn

Comments

All terms > 1 are divisible by 3. - Robert Israel, Sep 05 2014

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Eric Weisstein's World of Mathematics, Near-Square Prime

Crossrefs

Equals 6*A056900(n-2) + 3, n>1.

Cf. A106571, A040976.

Other sequences of the type "Numbers k such that k^2 + i is prime": A005574 (i=1), this sequence (i=2), A049422 (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

Maple

select(t -> isprime(t^2+2), [0,1,seq(3*i,i=1..1000)]); # Robert Israel, Sep 05 2014

Mathematica

lst={};Do[If[PrimeQ[n^2+2], AppendTo[lst, n]], {n, 3*10^2}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)
Join[{0, 1}, Select[Range[3, 1000, 6], PrimeQ[#^2 + 2] &]] (* Zak Seidov, Jan 30 2014 *)

PARI

select(n -> isprime(n^2+2),[1..500]) \\ Edward Jiang, Sep 05 2014