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 A038552 #50 Feb 16 2025 08:32:38
%S A038552 163,427,907,1555,2683,3763,5923,6307,10627,13843,15667,17803,20563,
%T A038552 30067,34483,31243,37123,48427,38707,58507,61483,85507,90787,111763,
%U A038552 93307,103027,103387,126043,166147,134467,133387,164803,222643,189883
%N A038552 Largest squarefree number k such that Q(sqrt(-k)) has class number n.
%C A038552 Conjecture: this is also the largest absolute value of negative fundamental discriminant d for class number n. This is to say, for even n, let k be the largest odd number such that h(-k) = n (if it exists), k' be the largest even number such that h(-k') = n (if it exists), then k > k'; here h(D) is the class number of the quadratic field with discriminant D. [Comment rewritten by _Jianing Song_, Oct 03 2022]
%C A038552 Numbers so far are all 19 mod 24. - _Ralf Stephan_, Jul 07 2003
%H A038552 Charles R Greathouse IV, <a href="/A038552/b038552.txt">Table of n, a(n) for n = 1..100</a>
%H A038552 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 A038552 Ralf Stephan, <a href="https://arxiv.org/abs/math/0409509">Prove or disprove. 100 Conjectures from the OEIS</a>, #16, arXiv:math/0409509 [math.CO], 2004.
%H A038552 M. Watkins, <a href="http://dx.doi.org/10.1090/S0025-5718-03-01517-5">Class numbers of imaginary quadratic fields</a>, Mathematics of Computation 73 (2004), pp. 907-938.
%H A038552 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%t A038552 << NumberTheory`NumberTheoryFunctions`; a = Table[0, {32} ]; Do[ If[ Mod[n, 4] != 1 || Mod[n, 4] != 2 || SquareFreeQ[n], c = ClassNumber[ -n]; If[c < 33, a[[c]] = n]], {n, 0, 250000} ]; a
%o A038552 (PARI) lista() = {my(nn=10^7, NMAX=100, v = vector(NMAX), c); for (k=1, nn, if (isfundamental(-k), if ((c = qfbclassno(-k)) <= NMAX, v[c]=k););); v;} \\ _Michel Marcus_, Feb 17 2022; takes several minutes
%Y A038552 Cf. A081319, A046125.
%K A038552 nonn,nice,hard
%O A038552 1,1
%A A038552 Robert Brewer (rbrewerjr(AT)aol.com)
%E A038552 More terms from _Robert G. Wilson v_, Nov 08 2001
%E A038552 2 more terms from _Dean Hickerson_, May 20 2003. The values were obtained by transcribing and combining data from Tables 1-3 of Buell's paper, which has information for all values of n up to 125.
%E A038552 Values checked against Watkins' data, which proves the values of a(n) for n = 1..100. _Charles R Greathouse IV_, Feb 08 2012