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Discriminants of imaginary quadratic fields with class number 19 (negated).
6

%I #20 Dec 25 2018 11:29:29

%S 311,359,919,1063,1543,1831,2099,2339,2459,3343,3463,3467,3607,4019,

%T 4139,4327,5059,5147,5527,5659,6803,8419,8923,8971,9619,10891,11299,

%U 15091,15331,16363,16747,17011,17299,17539,17683,19507,21187,21211,21283,23203,24763,26227,27043,29803,31123,37507,38707

%N Discriminants of imaginary quadratic fields with class number 19 (negated).

%C 47 discriminants in this sequence (proved).

%H Steven Arno, M. L. Robinson, Ferrell S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arith. 83 (1998) 295-330.

%H Duncan A. Buell, <a href="https://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 Keith Matthews, <a href="http://www.numbertheory.org/classnos/">Tables of imaginary quadratic fields with small class numbers</a>

%H C. Wagner, <a href="https://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 < 40000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 19, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* _Jean-François Alcover_, Oct 05 2012 *)

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

%K nonn,fini,full

%O 1,1

%A _Eric W. Weisstein_