[seqfan] Re: Alien Coding article

Georg.Fischer georg.fischer at t-online.de
Wed Feb 1 17:37:06 CET 2023

Hi SeqFans,

there are already similar attempts to derive
programs or relations automatically from the OEIS data,
most notably:
- the LODA project of Christian Krause et al.
   <https://loda-lang.org/>, for which I currently
   count 115433 programs derived from the OEIS data
   AND the b-files,
and also, as mentioned by Andrej,
- <http://sequencedb.net/statistics.html> of Jon Maiga,
   with an OEIS coverage of 77%

There is a number of cases where a sequence only seems
to follow some pattern, but it deviates from it at
rather high terms, for example:
   %C A327055 Sequence deviates from A140480 (RMS numbers);
   first deviation is at a(461)
In Sean Irvine's project jOEIS <https://github.com/archmageirvine/joeis> 
we have 153439 Java (~ 42.6 %) classes currently, all written more or 
less manually, from proven formulas, and checked against the b-files.

I maintain a subset of parameters (signatures) for linear/holonomic
recurrences that currently generates about 50.000 OEIS
sequences with a single program. I estimate another
set of 20.000 - 30.000 such parameters that we had implemented
differently in jOEIS (for example Brian Galebach's 6094 tilings),
but which (most probably) also can be generated by recurrences.
More generally I think that all sequences that have a g.f.,
resp. that "satisfy" some equation are sufficiently understood.

Nevertheless we have large sets of sequences without formulas
and programs, or with conjectured formulas only. For example,
from one author with ~40.000 sequences we did not - yet -
manage to implement more than ~4.000 in jOEIS, although they
are well defined, and often perhaps computable by recurrences

So - in my view - real progress in mathematical understanding
will not be achieved by "guessing" formulas from the OEIS data
terms, but by finding more groups with common formulas resp.

Regards - Georg

Am 01.02.2023 um 03:32 schrieb hv at crypt.org:
> I had a brief look through it. 
> The headline claim of 78000 sequences ...

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