[seqfan] Re: Sequences that need b-files
Maximilian Hasler
maximilian.hasler at gmail.com
Sun Mar 25 18:52:36 CEST 2012
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
>>>>
>>>>
>>
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>>
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>>
>
>
>
> --
> 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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