%I #15 Apr 12 2019 18:54:03

%S 449,673,977,1409,1873,2017,2081,2129,2417,2657,2753,3313,3697,4001,

%T 4561,4657,4673,4817,4993,6689,6833,7057,7121,7393,7457,7793,8017,

%U 8353,8369,8689,8849,9377,9473,9857,10193,10273,11057,11393,11489,11953,12161,12289

%N Prime numbers congruent to 1, 65 or 81 modulo 112 representable by both x^2 + 14*y^2 and x^2 + 448*y^2.

%C Brink showed that prime numbers congruent to 1, 65 or 81 modulo 112 are representable by both or neither of the quadratic forms x^2 + 14*y^2 and x^2 + 448*y^2. This sequence corresponds to those representable by both, and A325084 corresponds to those representable by neither.

%H David Brink, <a href="https://doi.org/10.1016/j.jnt.2008.04.007">Five peculiar theorems on simultaneous representation of primes by quadratic forms</a>, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893.

%H Rémy Sigrist, <a href="/A325083/a325083.gp.txt">PARI program for A325083</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>

%e Regarding 3313:

%e - 3313 is a prime number,

%e - 3313 = 29*112 + 65,

%e - 3313 = 53^2 + 14*6^2 = 39^2 + 448*2^2,

%e - hence 3313 belongs to this sequence.

%o (PARI) See Links section.

%Y See A325067 for similar results.

%Y Cf. A325084.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Mar 28 2019