A046011 Discriminants of imaginary quadratic fields with class number 14 (negated).

215, 287, 391, 404, 447, 511, 535, 536, 596, 692, 703, 807, 899, 1112, 1211, 1396, 1403, 1527, 1816, 1851, 1883, 2008, 2123, 2147, 2171, 2335, 2427, 2507, 2536, 2571, 2612, 2779, 2931, 2932, 3112, 3227, 3352, 3579, 3707, 3715, 3867, 3988

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• fini

Comments

There are 95 discriminants in this sequence (almost certainly but not proved).

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..95
• 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.
• Eric Weisstein's World of Mathematics, Class Number.
• Index entries for sequences related to quadratic fields

Crossrefs

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

Programs

Mathematica

Reap[ For[n = 1, n < 4000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 14, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

PARI

ok(n)={isfundamental(-n) && qfbclassno(-n) == 14} \\ Andrew Howroyd, Jul 24 2018