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.

A325072 Prime numbers congruent to 1 modulo 20 neither representable by x^2 + 20*y^2 nor by x^2 + 100*y^2.

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%I A325072 #20 Feb 25 2025 09:13:45
%S A325072 41,61,241,281,421,601,641,661,701,821,881,1181,1201,1301,1321,1381,
%T A325072 1481,1801,1901,2141,2161,2221,2281,2341,2381,2521,2741,3041,3061,
%U A325072 3181,3221,3361,3541,3701,3761,4241,4261,4421,4481,4721,4801,5381,5501,5521,5581
%N A325072 Prime numbers congruent to 1 modulo 20 neither representable by x^2 + 20*y^2 nor by x^2 + 100*y^2.
%C A325072 Brink showed that prime numbers congruent to 1 modulo 20 are representable by both or neither of the quadratic forms x^2 + 20*y^2 and x^2 + 100*y^2. A325071 corresponds to those representable by both, and this sequence corresponds to those representable by neither.
%H A325072 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 A325072 Akihide Hanaki, Kenji Kobayashi, and Akihiro Munemasa, <a href="https://arxiv.org/abs/2502.13331">3-Designs from PSL(2,q) with cyclic starter blocks</a>, arXiv:2502.13331 [math.CO], 2025. See pp. 2, 9, 13.
%H A325072 Rémy Sigrist, <a href="/A325072/a325072.gp.txt">PARI program for A325072</a>
%H A325072 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325072 Regarding 2221:
%e A325072 - 2221 is a prime number,
%e A325072 - 2221 = 111*20 + 1,
%e A325072 - 2221 is neither representable by x^2 + 20*y^2 nor by x^2 + 100*y^2,
%e A325072 - hence 2221 belongs to this sequence.
%o A325072 (PARI) \\ See Links section.
%Y A325072 See A325067 for similar results.
%Y A325072 Cf. A141881, A325071.
%K A325072 nonn
%O A325072 1,1
%A A325072 _Rémy Sigrist_, Mar 27 2019