A351680 - OEIS

%I #11 Feb 16 2025 08:34:03

%S 1959,2183,2911,3039,3176,3687,3831,4039,4103,4184,4735,4904,4952,

%T 5288,5935,5959,6179,6452,6487,6611,6623,6632,6836,7447,7604,7811,

%U 7892,7988,8459,8552,8579,8744,8852,9368,9428,9607,10231,10643,10772,10996,11023,11099

%N Discriminants of imaginary quadratic fields with class number 42 (negated).

%C Sequence contains 339 terms; largest is 280267.

%C The class group of Q[sqrt(-d)] is isomorphic to C_42 for all d in this sequence.

%H Andy Huchala, <a href="/A351680/b351680.txt">Table of n, a(n) for n = 1..339</a>

%H Mark Watkins, <a href="https://doi.org/10.1090/S0025-5718-03-01517-5">Class numbers of imaginary quadratic fields</a>, Mathematics of Computation, 73, pp. 907-938.

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

%o (Sage)

%o ls = [(QuadraticField(-n, 'a').discriminant(), QuadraticField(-n, 'a').class_number()) for n in (0..10000) if is_fundamental_discriminant(-n) and not is_square(n)];

%o [-a[0] for a in ls if a[1] == 42]

%Y Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664-A351679.

%K nonn,fini,full

%O 1,1

%A _Andy Huchala_, Mar 28 2022