[seqfan] Re: Sequences that need b-files

[David Wilson]

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.

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.

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?

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.
>>
>> Neil
>>