cp's OEIS Frontend

A046007 Discriminants of imaginary quadratic fields with class number 10 (negated).

%I A046007 #26 Feb 16 2025 08:32:38
%S A046007 119,143,159,296,303,319,344,415,488,611,635,664,699,724,779,788,803,
%T A046007 851,872,916,923,1115,1268,1384,1492,1576,1643,1684,1688,1707,1779,
%U A046007 1819,1835,1891,1923,2152,2164,2363,2452,2643,2776,2836,2899,3028
%N A046007 Discriminants of imaginary quadratic fields with class number 10 (negated).
%C A046007 87 discriminants in this sequence (almost certainly but not proved).
%H A046007 Andrew Howroyd, <a href="/A046007/b046007.txt">Table of n, a(n) for n = 1..87</a>
%H A046007 Steven Arno, M. L. Robinson and Ferrel S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arithm. 83.4 (1998), 295-330
%H A046007 Duncan A. Buell, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796.
%H A046007 C. Wagner, <a href="http://dx.doi.org/10.1090/S0025-5718-96-00722-3">Class Number 5, 6 and 7</a>, Math. Comput. 65, 785-800, 1996.
%H A046007 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>
%H A046007 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A046007 Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[14000], NumberFieldClassNumber[Sqrt[-#]] == 10 &]] (* _Jean-François Alcover_, Jun 27 2012 *)
%o A046007 (PARI) ok(n)={isfundamental(-n) && qfbclassno(-n) == 10} \\ _Andrew Howroyd_, Jul 24 2018
%o A046007 (Sage) [n for n in (1..3500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==10] # _G. C. Greubel_, Mar 01 2019
%Y A046007 Cf. A006203, A013658, A014602, A014603, A046002-A046020.
%Y A046007 Cf. A191410.
%K A046007 nonn,fini
%O A046007 1,1
%A A046007 _Eric W. Weisstein_