OFFSET
1,1
COMMENTS
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]
Numbers so far are all 19 mod 24. - Ralf Stephan, Jul 07 2003
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..100
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
Ralf Stephan, Prove or disprove. 100 Conjectures from the OEIS, #16, arXiv:math/0409509 [math.CO], 2004.
M. Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation 73 (2004), pp. 907-938.
Eric Weisstein's World of Mathematics, Class Number
MATHEMATICA
<< 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
PROG
(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
CROSSREFS
KEYWORD
nonn,nice,hard
AUTHOR
Robert Brewer (rbrewerjr(AT)aol.com)
EXTENSIONS
More terms from Robert G. Wilson v, Nov 08 2001
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.
Values checked against Watkins' data, which proves the values of a(n) for n = 1..100. Charles R Greathouse IV, Feb 08 2012
STATUS
approved