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%I #14 Sep 08 2022 08:45:45
%S 4,7,10,22,25,34,70,79,112,130,139,172,187,217,229,262,274,295,304,
%T 322,337,364,397,400,472,499,574,580,592,622,634,655,664,697,829,844,
%U 925,1057,1144,1165,1255,1300,1309,1357,1414,1420,1489,1537,1642,1669,1744
%N Numbers k such that k^2+k+3 and k^2+k-3 are both prime.
%H Daniel Starodubtsev, <a href="/A161863/b161863.txt">Table of n, a(n) for n = 1..10000</a>
%e 4 is in the list because 16+4+-3 = 23 and 17 are primes.
%e 7 is in the list because 49+7+-3 = 53 and 59 are primes.
%t q=3;lst3={};Do[p=n^2+n;If[PrimeQ[p-q]&&PrimeQ[p+q],AppendTo[lst3,n]],{n,0,7!}];lst3
%t Select[Range[2000],AllTrue[#^2+#+{3,-3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 01 2019 *)
%o (Magma) [k:k in [1..1750]| IsPrime(k^2+k+3) and IsPrime(k^2+k-3)]; // _Marius A. Burtea_, Feb 17 2020
%Y Cf. A088485, A027752
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 20 2009
%E Definition rephrased by _R. J. Mathar_, Jun 27 2009
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