A094619 Fundamental discriminants of real quadratic number fields with class number 2.

40, 60, 65, 85, 104, 105, 120, 136, 140, 156, 165, 168, 185, 204, 205, 220, 221, 232, 264, 265, 273, 280, 285, 296, 305, 312, 345, 348, 357, 364, 365, 377, 380, 385, 408, 424, 429, 440, 444, 456, 460, 465, 476, 481, 485, 488, 492, 493, 533, 545, 552, 561, 565

Offset: 1

Author

Eric W. Weisstein, May 14 2004

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
• Eric Weisstein's World of Mathematics, Class Number
• Index entries for sequences related to quadratic fields

Crossrefs

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

Programs

Mathematica

Select[Range[565], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 2 &] (* Arkadiusz Wesolowski, Oct 22 2012 *)

PARI

is(n)=n>9 && isfundamental(n) && qfbclassno(n)==2 \\ Charles R Greathouse IV, Nov 05 2014

Sage

is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 2;
A094619 = lambda n: filter(is_fund_and_qfbcn_1, (1, 2, .., n));
A094619(600) # G. C. Greubel, Mar 01 2019