A046013 - OEIS

%I #26 Dec 31 2018 08:19:27

%S 399,407,471,559,584,644,663,740,799,884,895,903,943,1015,1016,1023,

%T 1028,1047,1139,1140,1159,1220,1379,1412,1416,1508,1560,1595,1608,

%U 1624,1636,1640,1716,1860,1876,1924,1983,2004,2019,2040,2056,2072

%N Discriminants of imaginary quadratic fields with class number 16 (negated).

%C 322 discriminants in this sequence (almost certainly but not proved).

%H Andrew Howroyd, <a href="/A046013/b046013.txt">Table of n, a(n) for n = 1..322</a>

%H 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 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 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 Victor Y. Wang, <a href="http://arxiv.org/abs/1508.06552">On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields</a>, arXiv preprint arXiv:1508.06552, 2015

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%t Reap[ For[n = 1, n < 3000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 16, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* _Jean-François Alcover_, Oct 05 2012 *)

%o (PARI) ok(n)={isfundamental(-n) && qfbclassno(-n) == 16} \\ _Andrew Howroyd_, Jul 24 2018

%Y Cf. A006203, A013658, A014602, A014603, A046002-A046020.

%K nonn,fini

%O 1,1

%A _Eric W. Weisstein_