A046009 - OEIS

%I #25 Mar 15 2019 22:52:10

%S 231,255,327,356,440,516,543,655,680,687,696,728,731,744,755,804,888,

%T 932,948,964,984,996,1011,1067,1096,1144,1208,1235,1236,1255,1272,

%U 1336,1355,1371,1419,1464,1480,1491,1515,1547,1572,1668,1720,1732

%N Discriminants of imaginary quadratic fields with class number 12 (negated).

%C 206 discriminants in this sequence (almost certainly but not proved).

%H Andrew Howroyd, <a href="/A046009/b046009.txt">Table of n, a(n) for n = 1..206</a>

%H Steven Arno, M. L. Robinson and Ferrel S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arithm. 83.4 (1998), 295-330

%H Duncan A. Buell, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796.

%H C. Wagner, <a href="http://dx.doi.org/10.1090/S0025-5718-96-00722-3">Class Number 5, 6 and 7</a>, Math. Comput. 65, 785-800, 1996.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%t Reap[ For[n = 1, n < 2000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 12, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* _Jean-François Alcover_, Oct 05 2012 *)

%o (PARI) ok(n)={isfundamental(-n) && qfbclassno(-n) == 12} \\ _Andrew Howroyd_, Jul 24 2018

%o (Sage) [n for n in (1..3000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==12] # _G. C. Greubel_, Mar 01 2019

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

%Y Cf. A191410.

%K nonn,fini

%O 1,1

%A _Eric W. Weisstein_