A161866 Numbers k such that k^2+k+7 and k^2+k-7 are both prime.

3, 5, 9, 12, 24, 29, 32, 39, 44, 50, 57, 59, 65, 102, 135, 137, 144, 170, 180, 207, 260, 267, 297, 302, 305, 344, 347, 360, 365, 369, 389, 404, 429, 464, 474, 495, 540, 555, 570, 612, 620, 659, 662, 689, 767, 774, 792, 824, 837, 872, 885, 900, 950, 954, 989

Offset

1,1

Links

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

Example

a(1)=3 as 12+-7 are primes. a(2)=5 as 30+-7 are primes.

Mathematica

q=7; lst7={}; Do[p=n^2+n; If[PrimeQ[p-q]&&PrimeQ[p+q], AppendTo[lst7, n]], {n, 0, 7!}]; lst7
Select[Range[1000], AllTrue[#^2+#+{7, -7}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 26 2021 *)

Prog

(Magma) [k:k in [1..1000]| IsPrime(k^2+k+7) and IsPrime(k^2+k-7)]; // Marius A. Burtea, Feb 17 2020

Crossrefs

Cf. A088485, A161863, A161864, A153417.

Sequence in context: A059093 A084593 A275843 * A102968 A180341 A348746

Adjacent sequences: A161863 A161864 A161865 * A161867 A161868 A161869

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jun 20 2009

Extensions

Definition rephrased by R. J. Mathar, Jun 23 2009

Status

approved