[seqfan] Re: Changes to b-files and the rules [b-file lengths]

Chris Thompson cet1 at cam.ac.uk
Thu Nov 22 21:42:30 CET 2018

Extract from Neil Gruber's message of 14 November:

>3) B-files should have appealing, and generally "nice", lengths. The
>most often seen lengths are 1000 terms, 2500 in some case when higher
>amount of terms is time consuming, 5000 and 10000 terms. Term lengths
>for triangles, for a typical triangle of anti-diagonal, follow the
>pattern binomial(n+1,2) for n rows. Not-so-nice term lengths may occur
>when the digit length nears 1000 decimal places sooner than a typical
>length of 1000 terms.

(and later)

>3) A bulletin should be added which reads (or near to) " B-files of
>length larger than 10000 terms needs to be approved by and EIC unless
>otherwise directed by an EIC or bureaucrat.

This caused me to look at b-files that I have submitted in the past with
un-"nice" lengths. I found essentially two cases:

A030979 is the n such that C(2n,n) is coprime to 3*5*7. These have a
distinctly fractal distribution, with large gaps. I think I was planning
on a b-file of at least 1000 entries, but big gaps occur after 699 values
and then after 1374. It seemed quite unnatural to chop the b-file off
in the middle of a cluster.

There is a set of 10 sequences related to the "sum of n consecutive squares
equalling a square" problem, which one could arrange as

   A001032  A001033  A134419  (n values)
   A007475  A056131     -     (corresponding x values)
   A076215  A056132     -     (corresponding y values)
   A274469  A274470  A274471  ("missing" n values)

The b-files I submitted were for all n values up to 250000 (earlier 30000)
which makes the lengths not particularly "nice" (and some of them are
a little over 10000). The values for the different columns are computed
by a single program (using the Pellian equation described in A134419).
I suppose it would have been possible to truncate the results to
individually "nice" lengths, but it didn't seem natural to me at the
time. In any case, the sequences in the last row ("missing" n values)
would not have "nice" lengths unless the upper limit chosen were different
from those in the first row, which seems even less natural. 

Chris Thompson
Email: cet1 at cam.ac.uk

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