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A097698
Numbers k such that both 4*k^2 - 3 and 4*k^2 + 3 are primes.
7
2, 4, 5, 7, 32, 46, 56, 70, 73, 86, 109, 149, 152, 161, 163, 170, 175, 178, 208, 220, 235, 254, 277, 280, 290, 313, 317, 326, 334, 343, 347, 352, 364, 368, 373, 385, 403, 409, 434, 446, 460, 527, 541, 551, 565, 578, 598, 628, 632, 689, 709, 710, 737, 761, 812
OFFSET
1,1
LINKS
FORMULA
a(n) = A153975(n) / 2. - Vladimir Joseph Stephan Orlovsky, Apr 23 2010
MATHEMATICA
Select[Range[0, 7! ], PrimeQ[ #^2-3]&&PrimeQ[ #^2+3]&]/2 (* Vladimir Joseph Stephan Orlovsky, Apr 23 2010 *)
Select[Range[1000], AllTrue[4#^2+{3, -3}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 08 2019 *)
PROG
(Magma) [n: n in [1..1000] |IsPrime(4*n^2-3) and IsPrime(4*n^2+3)]; // Vincenzo Librandi, Nov 16 2010
(PARI) is(n)=isprime(4*n^2-3) && isprime(4*n^2+3) \\ Charles R Greathouse IV, Sep 27 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Carl R. White, Aug 20 2004
STATUS
approved