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

Author

Eric W. Weisstein, May 14 2004

Keywords

• nonn

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

Crossrefs

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

Programs

Mathematica

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

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

Extensions

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