A028870 Numbers k such that k^2 - 2 is prime.

2, 3, 5, 7, 9, 13, 15, 19, 21, 27, 29, 33, 35, 37, 43, 47, 49, 55, 61, 63, 69, 71, 75, 77, 89, 93, 103, 107, 117, 119, 121, 127, 131, 135, 139, 145, 155, 161, 169, 173, 177, 183, 191, 205, 211, 217, 223, 231, 233, 237, 239, 247, 253, 257, 259, 265, 267, 273, 279, 285

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• easy

Comments

It is conjectured that this sequence is infinite.

Primes 2,3,5,7,13,... are in A062326. - Zak Seidov, Oct 05 2014

Examples

			5^2 - 2 = 23 is prime, so 5 is in the sequence.
		

References

• D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000
• P. De Geest, Palindromic Quasipronics of the form n(n+x)
• Eric Weisstein's World of Mathematics, Near-Square Prime

Crossrefs

Cf. A028871.

Programs

Magma

[n: n in [1..1000] |IsPrime( n^2 - 2)]; // Vincenzo Librandi, Nov 18 2010

Maple

select(k->isprime(k^2-2),[$1..300]); # Muniru A Asiru, Jul 15 2018

Mathematica

a[n_]:=n^x-y;lst={};x=2;y=2;Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,0,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 03 2009 *)
Select[Range[300],PrimeQ[#^2-2]&] (* Harvey P. Dale, Mar 21 2013 *)

PARI

is(n)=isprime(n^2-2) \\ Charles R Greathouse IV, Jul 01 2013

Formula

a(n) = sqrt(2 + A028871(n)). - Zak Seidov, Oct 05 2014