A240878 Numbers n such that (n^2 + 2)/3 is prime.

2, 7, 11, 17, 29, 35, 37, 43, 53, 55, 65, 73, 79, 83, 97, 115, 119, 125, 133, 137, 155, 161, 169, 187, 191, 205, 209, 233, 251, 263, 269, 271, 277, 281, 287, 295, 335, 343, 359, 361, 379, 385, 389, 395, 407, 413, 425, 433, 451, 461, 475, 479, 493, 505, 511, 521, 529, 541, 559, 577

Offset: 1

Author

Robert Israel, Apr 13 2014

Keywords

• nonn
• easy

Comments

If n == 1 mod 3, then (n - 1)/3 is in A086285.

Examples

			(2^2 + 2)/3 = 6/3 = 2, which is prime, so 2 is in the sequence.
(7^2 + 2)/3 = 51/3 = 17, which is prime, so 7 is in the sequence.
(11^2 + 2)/3 = 123/3 = 41, which is prime, so 11 is in the sequence.
(13^2 + 2)/3 = 171/3 = 57 = 3 * 19, which is not prime, so 13 is not in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A086285.

Programs

Magma

[2] cat [n: n in [4..600] | IsPrime((n^2 + 2) div 3)]; // Vincenzo Librandi, Jul 01 2014

Maple

N:= 10000; # to get all terms <= 3 N + 2
A240878:= select(t -> isprime((t^2+2)/3),{seq(seq(3*i+j,j=1..2),i=0..N)}):

Mathematica

Select[Range[500], PrimeQ[(#^2 + 2)/3] &] (* Alonso del Arte, Apr 13 2014 *)

PARI

is(n)=isprime((n^2+2)/3) \\ Charles R Greathouse IV, Jun 06 2017