Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Apr 12 2019 08:25:13
%S 101,181,401,461,521,541,761,941,1021,1061,1361,1601,1621,1721,1741,
%T 1861,2081,2441,2621,2801,2861,3001,3121,3301,3461,3581,3821,3881,
%U 4001,4021,4201,4441,4561,4621,4861,5021,5081,5101,5261,5281,5441,5741,5861,5981,6221
%N Prime numbers congruent to 1 modulo 20 representable by both x^2 + 20*y^2 and x^2 + 100*y^2.
%C 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. This sequence corresponds to those representable by both, and A325072 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="/A325071/a325071.gp.txt">PARI program for A325071</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 1601:
%e - 1601 is a prime number,
%e - 1601 = 80*20 + 1,
%e - 1601 = 39^2 + 20*2^2 = 1^2 + 100*4^2,
%e - hence 1601 belongs to this sequence.
%o (PARI) See Links section.
%Y See A325067 for similar results.
%Y Cf. A141881, A325072.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 27 2019