A123232 Numbers n such that (2*n)^2 + 1 and (2*n)^2 + 3 are both prime.

1, 2, 5, 7, 37, 47, 65, 67, 73, 80, 115, 128, 163, 170, 175, 203, 215, 220, 235, 292, 317, 343, 350, 352, 392, 430, 460, 493, 527, 535, 578, 605, 662, 670, 677, 683, 697, 710, 728, 730, 782, 850, 892, 908, 938, 1003, 1040, 1048, 1087, 1235, 1267, 1285, 1300

Offset

1,2

Links

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

Example

a(4) = 7 because 14^2 + 1 = 197 and 14^2 + 3 = 199 which are both prime.

Maple

for i from 1 to 1000 do if(isprime(i^2 +1) and isprime(i^2+3)) then print(i/2); end if; end do;

Mathematica

Select[Range[1300], AllTrue[(2#)^2+{1, 3}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 15 2016 *)

Prog

(Magma) [n: n in [0..6000] | IsPrime((2*n)^2+1)and IsPrime((2*n)^2+3)] // Vincenzo Librandi, Nov 13 2010

Crossrefs

Cf. A001359.

Sequence in context: A160621 A028432 A019409 * A042559 A197222 A379642

Adjacent sequences: A123229 A123230 A123231 * A123233 A123234 A123235

Keyword

nonn

Author

Ben Paul Thurston, Oct 06 2006

Status

approved