A161863 Numbers k such that k^2+k+3 and k^2+k-3 are both prime.

4, 7, 10, 22, 25, 34, 70, 79, 112, 130, 139, 172, 187, 217, 229, 262, 274, 295, 304, 322, 337, 364, 397, 400, 472, 499, 574, 580, 592, 622, 634, 655, 664, 697, 829, 844, 925, 1057, 1144, 1165, 1255, 1300, 1309, 1357, 1414, 1420, 1489, 1537, 1642, 1669, 1744

Offset

1,1

Links

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Example

4 is in the list because 16+4+-3 = 23 and 17 are primes.
7 is in the list because 49+7+-3 = 53 and 59 are primes.

Mathematica

q=3; lst3={}; Do[p=n^2+n; If[PrimeQ[p-q]&&PrimeQ[p+q], AppendTo[lst3, n]], {n, 0, 7!}]; lst3
Select[Range[2000], AllTrue[#^2+#+{3, -3}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 01 2019 *)

Prog

(Magma) [k:k in [1..1750]| IsPrime(k^2+k+3) and IsPrime(k^2+k-3)]; // Marius A. Burtea, Feb 17 2020

Crossrefs

Cf. A088485, A027752

Sequence in context: A373655 A080922 A227686 * A102649 A084386 A275176

Adjacent sequences: A161860 A161861 A161862 * A161864 A161865 A161866

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jun 20 2009

Extensions

Definition rephrased by R. J. Mathar, Jun 27 2009

Status

approved