A177833 Numbers k such that k^2 - 13 and k^2 + 13 are primes.

4, 12, 18, 72, 84, 114, 198, 354, 378, 588, 612, 618, 864, 912, 948, 1032, 1068, 1134, 1320, 1410, 1428, 1452, 1500, 1830, 1956, 2046, 2058, 2172, 2298, 2448, 2634, 2748, 2844, 2856, 3192, 3246, 3390, 3474, 3846, 3906, 4092, 4182, 4506, 4842, 4884, 4890

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 14 2010

Keywords

• nonn

Examples

			4^2 - 13 = 3 = prime(2), 4^2 + 13 = 29 = prime(10).
12^2 - 13 = 131 = prime(32), 12^2 + 13 = 157 = prime(37).
948^2 - 13 = 898691 = prime(71194), 948^2 + 13 = prime(71195), first case that they are consecutive primes.
		

References

• J. Matousek and J. Nesetril, Diskrete Mathematik: eine Entdeckungsreise, Springer-Lehrbuch, 2. Aufl., Berlin, 2007

Links

• Zak Seidov, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A138375, A154648, A176969, A176978, A248785.

Programs

Magma

[n: n in [4..1000]| IsPrime(n^2-13) and IsPrime(n^2+13)]; // Vincenzo Librandi, Nov 30 2010

Maple

with(numtheory): A248785:=n->`if`(isprime(n^2-13) and isprime(n^2+13), n, NULL): seq(A248785(n), n=1..10^4); # Wesley Ivan Hurt, Oct 13 2014

Mathematica

Select[Range[2,5000,2],AllTrue[#^2+{13,-13},PrimeQ]&] (* Harvey P. Dale, May 28 2024 *)

Extensions

More terms from Vincenzo Librandi, May 16 2010

Name edited by Michel Marcus, Nov 25 2024