OFFSET
1,1
COMMENTS
Pythagorean primes p = x^2+y^2 where 3*x+y and |x-3*y| or x+3*y and |3*x-y| are primes.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 17 is a term because 170 = 7^2+11^2 with 17, 7 and 11 all prime.
MAPLE
filter:= proc(p) local F, a, b; uses GaussInt;
if not isprime(p) then return false fi;
F:= GIfactors(p)[2][1][1];
a:= abs(Re(F)); b:= abs(Im(F));
(isprime(a+3*b) and isprime(abs(3*a-b))) or (isprime(3*a+b) and isprime(abs(3*b-a)))
end proc:
select(filter, [seq(i, i=5..10000, 4)]);
MATHEMATICA
Select[Prime@Range@300, Select[PowersRepresentations[10#, 2, 2], And@@PrimeQ@#&]!={}&] (* Giorgos Kalogeropoulos, Aug 20 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Aug 20 2021
STATUS
approved