A094613 Fundamental discriminants of real quadratic number fields with class number 4.

145, 328, 445, 505, 520, 680, 689, 777, 780, 793, 840, 876, 897, 901, 905, 924, 1020, 1045, 1096, 1105, 1145, 1160, 1164, 1221, 1288, 1292, 1313, 1320, 1365, 1480, 1560, 1640, 1677, 1736, 1740, 1745, 1752, 1820, 1848, 1885, 1932, 2005, 2040, 2056, 2120, 2145

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[2145], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 4 &] (* Arkadiusz Wesolowski, Oct 22 2012 *)

Prog

(PARI) {ok(n) = n>10 && isfundamental(n) && qfbclassno(n)==4};
for(n=1, 2500, 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() == 4;
A094613 = lambda n: filter(is_fund_and_qfbcn_1, (1, 2, .., n));
A094613(2500) # G. C. Greubel, Mar 01 2019

Crossrefs

Cf. A003656, A094619, A094612, A094614, A218156-A218160.

Sequence in context: A177223 A318530 A158133 * A207058 A116208 A211470

Adjacent sequences: A094610 A094611 A094612 * A094614 A094615 A094616

Keyword

nonn

Author

Eric W. Weisstein, May 14 2004

Status

approved