A094612 Fundamental discriminants of real quadratic number fields with class number 3.

229, 257, 316, 321, 469, 473, 568, 733, 761, 892, 993, 1016, 1101, 1229, 1257, 1304, 1373, 1436, 1489, 1509, 1772, 1901, 1929, 1957, 2021, 2089, 2101, 2177, 2213, 2429, 2557, 2589, 2636, 2677, 2713, 2777, 2857, 2917, 2981, 3173, 3221, 3229, 3261, 3356, 3569

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Class Number

Index entries for sequences related to quadratic fields

Mathematica

Select[Range[3569], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 3 &] (* Arkadiusz Wesolowski, Oct 22 2012 *)

Prog

(PARI) {ok(n) = n>10 && isfundamental(n) && qfbclassno(n)==3};
for(n=1, 3600, if(ok(n)==1, print1(n, ", "))) \\ G. C. Greubel, Mar 01 2019
(Sage)
is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 3;
A094612 = lambda n: filter(is_fund_and_qfbcn_1, (1, 2, .., n));
A094612(3700) # G. C. Greubel, Mar 01 2019

Crossrefs

Cf. A003656, A094619, A094613-A094614, A218156-A218160.

Sequence in context: A342368 A250235 A250236 * A250237 A350165 A112847

Adjacent sequences: A094609 A094610 A094611 * A094613 A094614 A094615

Keyword

nonn

Author

Eric W. Weisstein, May 14 2004

Extensions

Edited by N. J. A. Sloane, May 01 2010

Status

approved