possible OEIS party Boston Apr 30?

[Tanya Khovanova]

On 4/6/07, Simon Plouffe <simon.plouffe at gmail.com> wrote:

>   I am curious about this result : A000041[n] up
> to 10^7. What did you used to compute these
> numbers? and how long did it took ?

I used the recurrent formula (11) at
http://mathworld.wolfram.com/PartitionFunctionP.html
keeping all computed values in a huge array.
At a system with 8GB physical memory I was able to compute 8.5M first
values until the process ate all memory and started swapping too
intensively.
Then Zak suggested to use high order differences in order to reduce
the required storage. So, instead of computing p(n), I computed the
200th order difference of p(n) (they satisfy the very same recurrent
formula). That reduced the memory usage enough to compute and store
10^7 first values (a text file with 10^7 first 200th-order differences
takes 17GB while a similar file with values of p(n) takes 23GB). Then
I restored values of p(n) out of their differences.

> and I offer the necessary bandwith to store
> your result about A000041 : I think I can manage to
> put a few more gigabytes on that disk.

That would be great!
I will keep this data online only for a month or so, and transferring
them to a permanent hosting is a good idea.

Here is the data. It is a text b-file p10_7.dat, compressed with bzip2
archiver. The resulting archive p10_7.dat.bz2 was split into ten
1GB-parts for better downloading and integrity checking. It can be
merged back into a single file with the standard "cat" (under *nix OS)
or "copy /b" (dos-like or windows OS) commands.

http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.001
http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.002
http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.003
http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.004
http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.005
http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.006
http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.007
http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.008
http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.009
http://dooku2.ucsd.edu/maxal/p10_7.dat.bz2.010

And these are MD5 sums:
8613a7196a7027153b5005d4d91b9ce3  p10_7.dat.bz2.001
367ca3d3d1ce5525eb3b631f975473d5  p10_7.dat.bz2.002
eda16376905b0d38a9a9f6be51b12d2a  p10_7.dat.bz2.003
be80be17f303dced214a34b7338c518f  p10_7.dat.bz2.004
1bf14dba381cfdeb380138ff5a1d8515  p10_7.dat.bz2.005
3f856edaf0cf3c88a3efd6822ab2f482  p10_7.dat.bz2.006
bf4efef2d9282a035fa3779456b8ec03  p10_7.dat.bz2.007
4aa1dab97e14d9a697f408def6ea8fe0  p10_7.dat.bz2.008
45b65d617e17db6df8dd95329a6b1f5c  p10_7.dat.bz2.009
9f5ff41b34e05321e549ad8a25a43260  p10_7.dat.bz2.010

Max