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

Author

Carl R. White, Aug 20 2004

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A083022, A097697, A153975.

Programs

Magma

[n: n in [1..1000] |IsPrime(4*n^2-3) and IsPrime(4*n^2+3)]; // Vincenzo Librandi, Nov 16 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 *)

PARI

is(n)=isprime(4*n^2-3) && isprime(4*n^2+3) \\ Charles R Greathouse IV, Sep 27 2016

Formula

a(n) = A153975(n) / 2. - Vladimir Joseph Stephan Orlovsky, Apr 23 2010