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
Examples
a(1)=3 as 12+-7 are primes. a(2)=5 as 30+-7 are primes.
Links
- Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Programs
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Magma
[k:k in [1..1000]| IsPrime(k^2+k+7) and IsPrime(k^2+k-7)]; // Marius A. Burtea, Feb 17 2020
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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 *)
Extensions
Definition rephrased by R. J. Mathar, Jun 23 2009