Sequence idea (fwd)

[Richard Guy]

Duncan Buell asked me to forward this message,
as it was bounced to him.

---------- Forwarded message ----------
Date: Wed, 26 Feb 2003 13:02:32 -0500
From: "BUELL, DUNCAN A" <BUELL at engr.sc.edu>
To: 'Richard Guy' <rkg at cpsc.ucalgary.ca>, buell at cse.sc.edu,
     buell at member.ams.org
Cc: seqfan at ext.jussieu.fr
Subject: RE: Sequence idea (fwd)

The first and last of many of these are in my paper,
D. A. Buell,
``Small class numbers and extreme values of $L$-functions of quadratic
fields,''
{\it Mathematics of Computation},
v. 31, 1977, pp. 786-796.

To the word "last" must be qualified with an appeal to
the Riemann hypothesis in many instances.  If these are
not in fact the last, then many of us will be very very
surprised...

Duncan A. Buell
Professor and Chair
Department of Computer Science and Engineering
University of South Carolina
Columbia, South Carolina  29208
803-777-2880 voice, 803-777-3767 fax
buell at cse.sc.edu, buell at engr.sc.edu, buell at sc.edu


-----Original Message-----
From: Richard Guy [mailto:rkg at cpsc.ucalgary.ca]
Sent: Wednesday, February 26, 2003 12:58 PM
To: buell at cse.sc.edu; buell at member.ams.org
Cc: seqfan at ext.jussieu.fr
Subject: Re: Sequence idea (fwd)


I got Duncan's email address(es) wrong just now.  R.

---------- Forwarded message ----------
Date: Wed, 26 Feb 2003 10:49:38 -0700 (MST)
From: Richard Guy <rkg at cpsc.ucalgary.ca>
To: David Wilson <davidwwilson at attbi.com>
Cc: Sequence Fanatics <seqfan at ext.jussieu.fr>, duncan at super.org
Subject: Re: Sequence idea

The corresponding sequence for real fields is

1,4,9,16,25,36,49,64,81,100,

I believe.  But Hugh Williams has just noted that
a far more interesting sequence would be the
largest such  k.  He says that Duncan Buell
(duncan at super.org) may know the answer to
this, up to the hundreds.    R.

On Wed, 26 Feb 2003, David Wilson wrote:

> Smallest k such that Q(sqrt(-k)) has class number n.
> For n = 1 through 10, i think we get 1,5,23,14,47,26,71,41,199,74
> I don't have the machinery to extend this one
> I don't even know if the domain is N.
> 
> Also, the analogous sequence for Q(sqrt(n)) would be good.