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A038552
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Largest number k such that Q(sqrt(-k)) has class number n.
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4
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163, 427, 907, 1555, 2683, 3763, 5923, 6307, 10627, 13843, 15667, 17803, 20563, 30067, 34483, 31243, 37123, 48427, 38707, 58507, 61483, 85507, 90787, 111763, 93307, 103027, 103387, 126043, 166147, 134467, 133387, 164803, 222643, 189883
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All terms are squarefree.
Probably all terms are odd, in which case this is also the largest absolute value of fundamental negative discriminant d for class number n.
Numbers so far are all 19 mod 24. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 07 2003
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REFERENCES
| Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
M. Watkins, "Class numbers of imaginary quadratic fields", Mathematics of Computation 73 (2004), pp. 907-938.
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LINKS
| Eric Weisstein's World of Mathematics, Class Number
Charles R Greathouse IV, Table of n, a(n) for n = 1..100
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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
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CROSSREFS
| Cf. A081319, A046125.
Sequence in context: A142427 A142237 A142283 * A127883 A054466 A002149
Adjacent sequences: A038549 A038550 A038551 * A038553 A038554 A038555
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KEYWORD
| nonn,nice,hard,changed
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AUTHOR
| Robert Brewer (rbrewerjr(AT)aol.com)
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EXTENSIONS
| More terms from rgwv(AT)rgwv.com (rgwv(AT)rgwv.com), Nov 08 2001
2 more terms from Dean Hickerson (dean.hickerson(AT)yahoo.com), 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
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