This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380102 #9 Jan 25 2025 23:01:11 %S A380102 3896,27156,423640,99888340 %N A380102 Minimal absolute discriminants |d| of imaginary quadratic number fields K = Q(sqrt(d)), d < 0, with elementary bicyclic 3-class group Cl_3(K)=(3,3) and second 3-class group M=Gal(F_3^2(K)/K) of assigned even coclass cc(M)=2,4,6,8,... %C A380102 The coclass cc(M) for the field K with discriminant d = -a(n) is 2*n, and for each field K with absolute discriminant |d| < a(n), the coclass cc(M) is less than 2*n. %H A380102 D. C. Mayer, <a href="http://arxiv.org/abs/1403.3833">The distribution of second p-class groups on coclass graphs</a>, arXiv:1403.3833 [math.NT], 2014; J. Théor. Nombres Bordeaux 25 (2013), 401-456. %H A380102 Daniel Constantin Mayer, <a href="/A380102/a380102.m.txt">Magma program "ImagCoClass.m" with endless loop</a> %F A380102 According to Theorem 3.12 on page 435 of "The distribution of second p-class groups on coclass graphs", the coclass of the group M is given by cc(M)+1=log_3(h_3(L_2)), where h_3(L_2) is the second largest 3-class number among the four unramified cyclic cubic extensions L_1,..,L_4 of the quadratic field K, and log_3 denotes the logarithm with respect to the basis 3. %e A380102 The coclass cannot be odd for imaginary quadratic fields. We have cc(M)=2 for d=-3896, cc(M)=4 for d=-27156, cc(M)=6 for d=-423640, cc(M)=8 for d=-99888340. %o A380102 (Magma) // See Links section. %Y A380102 Cf. A242862, A242863 (supersequences). Analog of A379524 for real quadratic fields. %K A380102 nonn,hard,more %O A380102 1,1 %A A380102 _Daniel Constantin Mayer_, Jan 12 2025