%I #13 Sep 08 2022 08:45:45
%S 3,5,9,12,24,29,32,39,44,50,57,59,65,102,135,137,144,170,180,207,260,
%T 267,297,302,305,344,347,360,365,369,389,404,429,464,474,495,540,555,
%U 570,612,620,659,662,689,767,774,792,824,837,872,885,900,950,954,989
%N Numbers k such that k^2+k+7 and k^2+k-7 are both prime.
%H Daniel Starodubtsev, <a href="/A161866/b161866.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=3 as 12+-7 are primes. a(2)=5 as 30+-7 are primes.
%t q=7;lst7={};Do[p=n^2+n;If[PrimeQ[p-q]&&PrimeQ[p+q],AppendTo[lst7,n]], {n,0,7!}];lst7
%t Select[Range[1000],AllTrue[#^2+#+{7,-7},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 26 2021 *)
%o (Magma) [k:k in [1..1000]| IsPrime(k^2+k+7) and IsPrime(k^2+k-7)]; // _Marius A. Burtea_, Feb 17 2020
%Y Cf. A088485, A161863, A161864, A153417.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 20 2009
%E Definition rephrased by _R. J. Mathar_, Jun 23 2009