A046016 Discriminants of imaginary quadratic fields with class number 19 (negated).

311, 359, 919, 1063, 1543, 1831, 2099, 2339, 2459, 3343, 3463, 3467, 3607, 4019, 4139, 4327, 5059, 5147, 5527, 5659, 6803, 8419, 8923, 8971, 9619, 10891, 11299, 15091, 15331, 16363, 16747, 17011, 17299, 17539, 17683, 19507, 21187, 21211, 21283, 23203, 24763, 26227, 27043, 29803, 31123, 37507, 38707

Offset

1,1

Comments

47 discriminants in this sequence (proved).

Links

Table of n, a(n) for n=1..47.

Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.

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

Keith Matthews, Tables of imaginary quadratic fields with small class numbers

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

Mathematica

Reap[ For[ n = 1, n < 40000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 19, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

Crossrefs

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

Sequence in context: A190567 A376235 A060339 * A142005 A059225 A157717

Adjacent sequences: A046013 A046014 A046015 * A046017 A046018 A046019

Keyword

nonn,fini,full

Author

Eric W. Weisstein

Status

approved