[seqfan] Re: Monotonic ordering of nonnegative differences

[Neil Sloane]

PS There are other sequences that are affected, e.g. Jinyuan Wang's
A321671, which is defined as the subset of primes in A192110.
What we do about that one?

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 Fri, Oct 11, 2019 at 11:37 AM Neil Sloane <njasloane at gmail.com> wrote:

> 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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>>
>