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.
%I A003657 M2332 #62 Aug 05 2025 10:34:07
%S A003657 3,4,7,8,11,15,19,20,23,24,31,35,39,40,43,47,51,52,55,56,59,67,68,71,
%T A003657 79,83,84,87,88,91,95,103,104,107,111,115,116,119,120,123,127,131,132,
%U A003657 136,139,143,148,151,152,155,159,163,164,167,168,179,183,184,187,191
%N A003657 Discriminants of imaginary quadratic fields, negated.
%C A003657 Negative of fundamental discriminants D := b^2-4*a*c<0 of definite integer binary quadratic forms F=a*x^2+b*x*y+c*y^2. See Buell reference pp. 223-234. See 4*A089269 = A191483 for even a(n) and A039957 for odd a(n). - _Wolfdieter Lang_, Nov 07 2003
%C A003657 All prime numbers in the set of the absolute values of negative fundamental discriminants are Gaussian primes (A002145). - _Paul Muljadi_, Mar 29 2008
%C A003657 Complement: 1, 2, 5, 6, 9, 10, 12, 13, 14, 16, 17, 18, 21, 22, 25, 26, 27, 28, 29, 30, 32, 33, 34, 36, ..., . - _Robert G. Wilson v_, Jun 04 2011
%C A003657 The asymptotic density of this sequence is 3/Pi^2 (A104141). - _Amiram Eldar_, Feb 23 2021
%D A003657 Duncan A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989.
%D A003657 Henri Cohen, A Course in Computational Algebraic Number Theory, Springer, 1993, p. 514.
%D A003657 Paulo Ribenboim, Algebraic Numbers, Wiley, NY, 1972, p. 97.
%D A003657 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003657 T. D. Noe, <a href="/A003657/b003657.txt">Table of n, a(n) for n=1..3000</a>
%H A003657 David Broadhurst and Daniele Dorigoni, <a href="https://arxiv.org/abs/2507.21352">Resurgent Lambert series with characters</a>, arXiv:2507.21352 [math.NT], 2025. See pp. 30, 53.
%H A003657 Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a>. [Cached copy, with permission of the author]
%H A003657 Rick L. Shepherd, <a href="http://libres.uncg.edu/ir/uncg/f/Shepherd_uncg_0154M_11099.pdf">Binary quadratic forms and genus theory</a>, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
%H A003657 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>, <a href="https://mathworld.wolfram.com/DirichletL-Series.html">Dirichlet L-Series</a>, <a href="https://mathworld.wolfram.com/FundamentalDiscriminant.html">Fundamental Discriminant</a>.
%t A003657 FundamentalDiscriminantQ[n_Integer] := n != 1 && (Mod[n, 4] == 1 || !Unequal[ Mod[n, 16], 8, 12]) && SquareFreeQ[n/2^IntegerExponent[n, 2]] (* via _Eric E. Weisstein_ *); -Select[-Range@ 194, FundamentalDiscriminantQ] (* _Robert G. Wilson v_, Jun 01 2011 *)
%o A003657 (PARI) ok(n)={isfundamental(-n)} \\ _Andrew Howroyd_, Jul 20 2018
%o A003657 (PARI) ok(n)={n<>1 && issquarefree(n/2^valuation(n,2)) && (n%4==3 || n%16==8 || n%16==4)} \\ _Andrew Howroyd_, Jul 20 2018
%o A003657 (Sage) [n for n in (1..200) if is_fundamental_discriminant(-n)==1] # _G. C. Greubel_, Mar 01 2019
%Y A003657 Cf. A002145, A003658, A039957 (odd terms), A191483 (even terms), A104141.
%K A003657 nonn
%O A003657 1,1
%A A003657 _N. J. A. Sloane_, _Mira Bernstein_