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

1,1

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A327687 A307623 A307624 * A166162 A228166 A244433

Adjacent sequences: A177830 A177831 A177832 * A177834 A177835 A177836

Keyword

nonn

Author

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

Extensions

More terms from Vincenzo Librandi, May 16 2010

Name edited by Michel Marcus, Nov 25 2024

Status

approved