A097698 Numbers k such that both 4*k^2 - 3 and 4*k^2 + 3 are primes.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A083022, A097697, A153975.

Sequence in context: A244332 A119909 A301521 * A233524 A324331 A101410

Adjacent sequences: A097695 A097696 A097697 * A097699 A097700 A097701

Keyword

easy,nonn

Author

Carl R. White, Aug 20 2004

Status

approved