[seqfan] Monotonic ordering of nonnegative differences

[israel at math.ubc.ca]

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