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%I #17 Apr 19 2019 13:45:38
%S 17,97,193,241,401,433,449,641,673,769,929,977,1009,1297,1361,1409,
%T 1489,1697,1873,2017,2081,2161,2417,2609,2753,2801,2897,3041,3169,
%U 3329,3457,3617,3697,3793,3889,4129,4241,4337,4561,4673,5009,5153,5281,5441,5521,5857
%N Prime numbers congruent to 1 modulo 16 representable neither by x^2 + 32*y^2 nor by x^2 + 64*y^2.
%C Kaplansky showed that prime numbers congruent to 1 modulo 16 are representable by both or neither of the quadratic forms x^2 + 32*y^2 and x^2 + 64*y^2. A325067 corresponds to those representable by both, and this sequence 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="/A325068/a325068.gp.txt">PARI program for A325068</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 17:
%e - 17 is a prime number,
%e - 17 = 16*1 + 1,
%e - 17 is representable neither by x^2 + 32*y^2 nor by x^2 + 64*y^2,
%e - hence 17 belongs to the sequence.
%o (PARI) See Links section.
%Y Cf. A094407, A325067.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 27 2019
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