[seqfan] Re: Monotonic ordering of nonnegative differences

[Neil Sloane]

Robert, thank you for catching those errors.  Yes, we will need to add a
comment.
Sadly, there are b-files too.  Should they be deleted, do you think?
Another thing: the complementary sequences are also in the OEIS, e.g.
A173671 ,
which is the complement of A192111, and was submitted by Max Alekseyev.
With a different search limit.  I will handle this, once we decide what to
do.  Any comments, anyone?

We have a rule that programs and b-files should not be based on
conjectures, so should the
programs be deleted too?

I really hope we can keep the sequences, and obviously if we keep the
sequences then we need to keep the programs, to show how they were
calculated.  But the b-files?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Thu, Oct 10, 2019 at 5:31 PM <israel at math.ubc.ca> wrote:

> There are 52 sequences from A192110 to A192202, contributed by Clark
> Kimberling, with Name of the form "Monotonic ordering of nonnegative
> differences a^i-b^j, for i>=0, j>=0" for various values of a and b.
>
> From the Mathematica code, it seems they are all computed by assuming i <=
> 40. I'm not aware of any theoretical justification for the assumption that
> any term in the range of the Data (which might go up to several million)
> will arise from i <= 40, although I have no counterexample and it may be
> unlikely that there is one. These are related to Catalan's conjecture
> (proved by Mihailescu), according to which 1 is not a member of any of
> these sequences unless i=1 or j<=1 works. There are also modular reasons
> for excluding some values (e.g. if prime p divides b but not a, then all
> terms divisible by p are of the form a^i-1). But for many values > 1, I
> don't think much is known rigorously.
>
> Should these sequences all get a Comment that the Data are conjectured?
>
> Cheers,
> Robert
>
>
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