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 A177833 Numbers n with the property p = n^2 - 13 and q = n^2 + 13 are primes. 5
 4, 12, 18, 72, 84, 114, 198, 354, 378, 588, 612, 618, 864, 912, 948, 1032, 1068, 1134, 1320, 1410, 1428, 1452, 1500, 1830, 1956, 2046, 2058, 2172, 2298, 2448, 2634, 2748, 2844, 2856, 3192, 3246, 3390, 3474, 3846, 3906, 4092, 4182, 4506, 4842, 4884, 4890 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES J. Matousek and J. Nesetril: Diskrete Mathematik: eine Entdeckungsreise, Springer-Lehrbuch, 2. Aufl., Berlin, 2007 LINKS Zak Seidov, Table of n, a(n) for n = 1..3000 EXAMPLE 4^2 - 13 = 3 = prime(2), 4^2 + 13 = 29 = prime(10). 12^2 - 13 = 131 = prime(32), 12^2 + 13 = 157 = prime(37). p = 948^2 - 13 = 898691 = prime(71194), q = prime(71195), first case that p and q are consecutive primes. MAPLE 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 MATHEMATICA Select[Range[5000], AllTrue[#^2+{13, -13}, PrimeQ]&] (* Harvey P. Dale, May 28 2024 *) PROG (Magma) [n: n in [4..1000]| IsPrime(n^2-13) and IsPrime(n^2+13)] // Vincenzo Librandi, Nov 30 2010 CROSSREFS Cf. A138375, A154648, A176969, A176978, A248785. Sequence in context: A327687 A307623 A307624 * A166162 A228166 A244433 Adjacent sequences: A177830 A177831 A177832 * A177834 A177835 A177836 KEYWORD nonn AUTHOR Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 14 2010 EXTENSIONS More terms from Vincenzo Librandi, May 16 2010 STATUS approved

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Last modified August 3 07:10 EDT 2024. Contains 374877 sequences. (Running on oeis4.)