|
%I #12 Apr 12 2019 18:54:30
%S 137,233,281,953,1033,1129,1481,2137,2377,2713,2857,2969,3529,3593,
%T 3833,4649,4729,5657,5737,5849,6217,6329,6521,6857,7001,7561,8089,
%U 8233,8297,8761,8969,9209,9241,9433,9689,10313,11113,12377,12457,12553,12601,12713,12889
%N Prime numbers congruent to 9, 25 or 57 modulo 112 representable by x^2 + 14*y^2.
%C Brink showed that prime numbers congruent to 9, 25 or 57 modulo 112 are representable by exactly one of the quadratic forms x^2 + 14*y^2 or x^2 + 448*y^2. This sequence corresponds to those representable by the first form, and A325086 corresponds to those representable by the second form.
%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="/A325085/a325085.gp.txt">PARI program for A325085</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 11113:
%e - 11113 is a prime number,
%e - 11113 = 99*112 + 25,
%e - 11113 = 103^2 + 14*6^2,
%e - hence 11113 belongs to this sequence.
%o (PARI) See Links section.
%Y See A325067 for similar results.
%Y Cf. A325086.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Mar 28 2019
|
