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.

A325081 Prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 representable by x^2 + x*y + 14*y^2.

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%I A325081 #13 Apr 12 2019 18:53:47
%S A325081 59,199,229,269,379,389,499,509,839,929,1049,1279,1409,1439,1499,1609,
%T A325081 1699,2029,2069,2269,2399,2699,2729,2819,3019,3089,3469,3529,3719,
%U A325081 4049,4079,4129,4139,4339,4519,4679,4789,4889,4999,5119,5399,5479,5669,6029,6229
%N A325081 Prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 representable by x^2 + x*y + 14*y^2.
%C A325081 Brink showed that prime numbers congruent to 4, 9, 14, 34 or 49 modulo 55 are representable by exactly one of the quadratic forms x^2 + x*y + 14*y^2 or x^2 + x*y + 69*y^2. This sequence corresponds to those representable by the first form, and A325082 corresponds to those representable by the second form.
%H A325081 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 A325081 Rémy Sigrist, <a href="/A325081/a325081.gp.txt">PARI program for A325081</a>
%H A325081 Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>
%e A325081 Regarding 4999:
%e A325081 - 4999 is a prime number,
%e A325081 - 4999 = 90*55 + 49,
%e A325081 - 4999 = 41^2 + 41*14 + 14*14^2,
%e A325081 - hence 4999 belongs to this sequence.
%o A325081 (PARI) See Links section.
%Y A325081 See A325067 for similar results.
%Y A325081 Cf. A325082.
%K A325081 nonn
%O A325081 1,1
%A A325081 _Rémy Sigrist_, Mar 28 2019