cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A325084 Prime numbers congruent to 1, 65 or 81 modulo 112 neither representable by x^2 + 14*y^2 nor by x^2 + 448*y^2.

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%I A325084 #15 Apr 12 2019 18:54:18
%S A325084 113,193,337,401,641,1009,1201,1297,2689,2801,3089,3137,3217,3329,
%T A325084 3361,3761,3889,4337,4481,5009,5153,5233,5441,5569,6113,6337,6353,
%U A325084 6449,6577,6673,7681,7841,8513,8737,8929,9041,9137,9521,9601,9697,10369,10529,10753
%N A325084 Prime numbers congruent to 1, 65 or 81 modulo 112 neither representable by x^2 + 14*y^2 nor by x^2 + 448*y^2.
%C A325084 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. A325083 corresponds to those representable by both, and this sequence corresponds to those representable by neither.
%H A325084 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 A325084 Rémy Sigrist, <a href="/A325084/a325084.gp.txt">PARI program for A325084</a>
%H A325084 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325084 Regarding 113:
%e A325084 - 113 is a prime number,
%e A325084 - 113 = 1*112 + 1,
%e A325084 - 113 is neither representable by x^2 + 14*y^2 nor by x^2 + 448*y^2,
%e A325084 - hence 113 belongs to this sequence.
%o A325084 (PARI) See Links section.
%Y A325084 See A325067 for similar results.
%Y A325084 Cf. A325083.
%K A325084 nonn
%O A325084 1,1
%A A325084 _Rémy Sigrist_, Mar 28 2019