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A028870 Numbers k such that k^2 - 2 is prime. 31
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is conjectured that this sequence is infinite.

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

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

FORMULA

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

EXAMPLE

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

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 *)

PROG

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

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

CROSSREFS

Cf. A028871.

Sequence in context: A080000 A032459 A263647 * A057886 A302835 A200672

Adjacent sequences:  A028867 A028868 A028869 * A028871 A028872 A028873

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified September 19 15:12 EDT 2018. Contains 315195 sequences. (Running on oeis4.)