[seqfan] Re: Sequences that need b-files
njasloane at gmail.com
Sun Mar 25 17:23:41 CEST 2012
David, I WILL TYPE MY REPLIES IN CAPS
On Sun, Mar 25, 2012 at 11:00 AM, David Wilson <davidwwilson at comcast.net>wrote:
> Sequences 18, 21, 24, 49, 50, 67, 72, 74, 75, 76 and 77 (and other
> sequences beyond the 1-100 range) are of the form
> Number of positive integers <= 2^n of form p(x, y)
> where p(x, y) is a quadratic polynomial (e.g. x^2 + y^2, x^2 + xy + y^2).
> I extended a few of these sequences myself (most anonymously) to full STU
> length some time ago. I observe that these sequences are difficult to
> compute (they have the aroma of prime-counting sequences), leastwise, I was
> unable to find any significant shortcuts (not that I am a brilliant number
> theorist). I doubt you are going to get b-file worthy extensions of these
> sequences, indeed, you might consider adding the "hard" keyword.
HARD IS SUPPOSED TO MEAN REALLY REALLY HARD, that the
next term is almost beyond reach. I don't think these are that hard.
You can compute them using theta series and/or modular forms.
> Regarding 92, Back in the day, before attribution was such a big deal, I
> extended 36, 99, 92 and 223 anonymously. I can attest that these are hard
> to extend (modulo my limited abilities), and perhaps a "hard" keyword is in
> order on these. I doubt we can generate enough elements to justify a b-file.
I DISAGREE - see above
> 34 is a simple periodic sequence. I remember at one time NJAS asked me not
> to included b-files for such sequences, as they were space-wasters. Has
> that policy changed? Perhaps we need a keyword indicating that a b-file is
WE HAVE ENOUGH KEYWORDS ALREADY. A000034 is not just any old periodic
sequence, it is an important one
> 63 is in the limbo of uncertain definition, it will not have a b-file
> until its definition is resolved.
> 44, 61, and 99 now have b-files.
> On Sun, Mar 25, 2012 at 6:40 AM, Neil Sloane <njasloane at gmail.com> wrote:
>> Seq Fans, Simon
>>> This morning I went through the first 100 sequences
>>> (A000001 - A000100) to see which ones could use b-files.
>>> Here is my list:
>>> (I leave out A0000)
>>> 18, 21, 24, 34, 44, 49, 50, 61, 63, 67, 72, 74, 75, 76, 77, 92, 95.
>>> If anyone would like to add these b-files, please do so - but of course
>>> be very careful, as always.
>>> For some of them we will first need to find what the exact definition is,
>>> before we can add a b-file. This means getting the precise definition
>>> from the original source.
> Seqfan Mailing list - http://list.seqfan.eu/
Dear Friends, I will soon be retiring from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
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Email: njasloane at gmail.com
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