login
A123232
Numbers n such that (2*n)^2 + 1 and (2*n)^2 + 3 are both prime.
1
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
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 A062645
KEYWORD
nonn
AUTHOR
Ben Paul Thurston, Oct 06 2006
STATUS
approved