[seqfan] Re: Sequences that need b-files
Neil Sloane
njasloane at gmail.com
Sun Mar 25 20:43:42 CEST 2012
well, I actually prefer the existing version, since to me it is easier
to understand (and of course I wrote it)!
and "hard" is not meant hard for the above-average reader (most
number-theoretic sequences are hard for that person). No, hard
means "really hard"!
Neil
On Sun, Mar 25, 2012 at 12:52 PM, Maximilian Hasler <
maximilian.hasler at gmail.com> wrote:
> The titles (%NAME) listed for http://oeis.org/search?q=A92 need cleanup...
>
> instead of
> %N Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) =
> (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); sequence gives values of n where
> |P(n)| sets a new record.
>
> I'd prefer something like
> %N Values of n where the (absolute) difference of A(n) = #{(i,j,k):
> i^2 + j^2 + k^2 <= n}, and V(n) = (4/3)Pi*n^(3/2) sets a new record.
>
> In principle the names A(n) and V(n) are not required in the title and
> I'd rather introduce them in a comment (or formula, example,...) in
> case they'd be used.
> But I don't want to make too radical changes...
>
> Second, the function V(n) is certainly "easy", thus the basic
> "interesting" sequence in this context is A(n) [or A( A92(n))], the
> rest is easy.
>
> Finally I'd partially agree with David on calling "hard" sequences
> that are difficult to compute for a random above-average reader, at
> least as long as they lack an explicit formula and/or program on OEIS.
> The subsequence of "really hard" sequences characterized by Neil as
> "next term almost beyond reach" can still be found as using
> "keyword:hard,more".
> (But I don't want to start a discussion on this.)
>
>
> Maximilian
>
>
>
> On Sun, Mar 25, 2012 at 11:23 AM, Neil Sloane <njasloane at gmail.com> wrote:
> > 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
> >> inappropriate?
> >>
> >
> > 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.
> >>
> >> THANKS!
> >>
> >
> > BEST REGARDS
> >
> > NEIL
> >
> >>
> >> 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.
> >>>>
> >>>> Neil
> >>>>
> >>>>
> >>
> >> ______________________________**_________________
> >>
> >> 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
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> 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
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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