[seqfan] Re: Potential improvements to existing OEIS Taxicab sequences

[M. F. Hasler]

On Tue, Jan 19, 2021 at 8:44 AM larry lacey <larryflacey at gmail.com> wrote:

> (3)    There is a simple method of mine that can be used to complete the
> sequences oeis.org/A003825 & oeis.org/A003826
>

Hi Larry,

did you notice that  A003825 already has 34204 terms listed?
So I'm not sure that it needs completion,
unless you want to say that there are missing terms within the list given
so far?
If you think so, please say this clearly (and if possible give the first
missing term(s)), it would be very important.
Since the b-file is from Ray Chandler I would tend to think it's correct,
but I didn't check.

OTOH, the Mmca code given by Orlovsky in ois.org/A018787 ("all solutions",
i.e., not only non-primitive) looks indeed faulty to me!
The list that code would produce should indeed be incomplete in the second
half, if I'm not wrong.
Specifically, if one lists solutions as large as  m^3+n^3 with  m<n<2000,
then one actually needs to go up to n = 2000 * 2^(1/3) ~ 2500 to be sure
one does not miss those which have 2nd and 3rd representations with much
smaller m.
But again, the b-file (here 100 000 terms !) was computed by Ray Chandler,
not by Orlovsky, so there's hope it's correct.
Please be more explicit if you have found an error in the database.

Thank you,

- Maximilian