cp's OEIS Frontend

A013658 Discriminants of imaginary quadratic fields with class number 4 (negated).

%I A013658 #36 Feb 16 2025 08:32:32
%S A013658 39,55,56,68,84,120,132,136,155,168,184,195,203,219,228,259,280,291,
%T A013658 292,312,323,328,340,355,372,388,408,435,483,520,532,555,568,595,627,
%U A013658 667,708,715,723,760,763,772,795,955,1003,1012,1027,1227,1243,1387,1411,1435,1507,1555
%N A013658 Discriminants of imaginary quadratic fields with class number 4 (negated).
%D A013658 H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 229.
%H A013658 Giovanni Resta, <a href="/A013658/b013658.txt">Table of n, a(n) for n = 1..54</a> (full sequence, from Weisstein's World of Mathematics)
%H A013658 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 A013658 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%H A013658 Sung Sik Woo, <a href="https://doi.org/10.4134/CKMS.2013.28.2.209">Cubic formula and cubic curves</a>, Commun. Korean Math. Soc. 28 (2013), No. 2, pp. 209-224.
%H A013658 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A013658 Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[1250], NumberFieldClassNumber[Sqrt[-#]] == 4 &]] (* _Jean-François Alcover_, Jun 27 2012 *)
%o A013658 (PARI) ok(n)={isfundamental(-n) && quadclassunit(-n).no == 4} \\ _Andrew Howroyd_, Jul 20 2018
%o A013658 (Sage) [n for n in (1..2000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==4] # _G. C. Greubel_, Mar 01 2019
%Y A013658 Cf. A014603, A046005, A192322.
%K A013658 nonn,fini,full
%O A013658 1,1
%A A013658 Eric Rains (rains(AT)caltech.edu)
%E A013658 a(50)-a(54) added by _Andrew Howroyd_, Jul 20 2018