A046013 Discriminants of imaginary quadratic fields with class number 16 (negated).

399, 407, 471, 559, 584, 644, 663, 740, 799, 884, 895, 903, 943, 1015, 1016, 1023, 1028, 1047, 1139, 1140, 1159, 1220, 1379, 1412, 1416, 1508, 1560, 1595, 1608, 1624, 1636, 1640, 1716, 1860, 1876, 1924, 1983, 2004, 2019, 2040, 2056, 2072

Offset

1,1

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..322

Steven Arno, M. L. Robinson and Ferrel S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arithm. 83.4 (1998), 295-330

Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.

C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.

Victor Y. Wang, On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields, arXiv preprint arXiv:1508.06552, 2015

Eric Weisstein's World of Mathematics, Class Number.

Index entries for sequences related to quadratic fields

Mathematica

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 *)

Prog

(PARI) ok(n)={isfundamental(-n) && qfbclassno(-n) == 16} \\ Andrew Howroyd, Jul 24 2018

Crossrefs

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

Sequence in context: A261768 A274446 A253598 * A352360 A176911 A202158

Adjacent sequences: A046010 A046011 A046012 * A046014 A046015 A046016

Keyword

nonn,fini

Author

Eric W. Weisstein

Status

approved