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.

A037449 Discriminant of quadratic field Q(sqrt(n)).

This page as a plain text file.
%I A037449 #41 May 16 2024 20:35:40
%S A037449 1,8,12,1,5,24,28,8,1,40,44,12,13,56,60,1,17,8,76,5,21,88,92,24,1,104,
%T A037449 12,28,29,120,124,8,33,136,140,1,37,152,156,40,41,168,172,44,5,184,
%U A037449 188,12,1,8,204,13,53,24,220,56,57,232,236,60,61,248,28,1,65,264,268,17,69
%N A037449 Discriminant of quadratic field Q(sqrt(n)).
%C A037449 For the discriminant of the quadratic field Q(sqrt(-n)), see A204993.
%C A037449 a(n) is the smallest positive N such that (n/k) = (n/(k mod N)) for every odd k that is coprime to n, where (n/k) is the Jacobi symbol. As we have Dirichlet's theorem on arithmetic progressions, a(n) is also the smallest positive N such that (n/p) = (n/(p mod N)) for every odd prime p that is not a factor of n. - _Jianing Song_, May 16 2024
%H A037449 T. D. Noe, <a href="/A037449/b037449.txt">Table of n, a(n) for n = 1..1000</a>
%H A037449 S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Class number theory</a>
%H A037449 Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]
%F A037449 Let b(n) = A007913(n), then a(n) = b(n) if b(n) == 1 (mod 4) and 4*b(n) otherwise. - _Jianing Song_, May 16 2024
%t A037449 Table[NumberFieldDiscriminant[Sqrt[n]], {n, 100}] (* _Artur Jasinski_, Jan 27 2012 *)
%o A037449 (PARI) vector(150,n,quaddisc(n))
%o A037449 (Sage)
%o A037449 [fundamental_discriminant(n) for n in (1..69)] # _Peter Luschny_, Oct 15 2018
%Y A037449 Cf. A204993, A007913.
%K A037449 nonn,easy
%O A037449 1,2
%A A037449 _Jason Earls_, Jun 30 2001