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A161863
Numbers k such that k^2+k+3 and k^2+k-3 are both prime.
3
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Definition rephrased by R. J. Mathar, Jun 27 2009
STATUS
approved