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%I #23 Nov 25 2024 11:59:59
%S 4,12,18,72,84,114,198,354,378,588,612,618,864,912,948,1032,1068,1134,
%T 1320,1410,1428,1452,1500,1830,1956,2046,2058,2172,2298,2448,2634,
%U 2748,2844,2856,3192,3246,3390,3474,3846,3906,4092,4182,4506,4842,4884,4890
%N Numbers k such that k^2 - 13 and k^2 + 13 are primes.
%D J. Matousek and J. Nesetril, Diskrete Mathematik: eine Entdeckungsreise, Springer-Lehrbuch, 2. Aufl., Berlin, 2007
%H Zak Seidov, <a href="/A177833/b177833.txt">Table of n, a(n) for n = 1..3000</a>
%e 4^2 - 13 = 3 = prime(2), 4^2 + 13 = 29 = prime(10).
%e 12^2 - 13 = 131 = prime(32), 12^2 + 13 = 157 = prime(37).
%e 948^2 - 13 = 898691 = prime(71194), 948^2 + 13 = prime(71195), first case that they are consecutive primes.
%p with(numtheory): A248785:=n->`if`(isprime(n^2-13) and isprime(n^2+13), n, NULL): seq(A248785(n), n=1..10^4); # _Wesley Ivan Hurt_, Oct 13 2014
%t Select[Range[2,5000,2],AllTrue[#^2+{13,-13},PrimeQ]&] (* _Harvey P. Dale_, May 28 2024 *)
%o (Magma) [n: n in [4..1000]| IsPrime(n^2-13) and IsPrime(n^2+13)]; // _Vincenzo Librandi_, Nov 30 2010
%Y Cf. A138375, A154648, A176969, A176978, A248785.
%K nonn
%O 1,1
%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 14 2010
%E More terms from _Vincenzo Librandi_, May 16 2010
%E Name edited by _Michel Marcus_, Nov 25 2024