Re: Project Euclid Problem 26 SOLVED!!!

On Tue, 12 Mar 2024 15:16:21 -0500, Physfitfreak wrote:

 
It provides a rare peep into how things are for larger integers at the
denominator of rational numbers. Not derived, but actually computed.
 
Then, somebody should derive such features by math alone, not computing.
At least the main features. It could be publishable too, if not derived
before. But I doubt it's something novel. Math people have done all
sorts of investigations, many of them even long ago.
 

If you want, I can provide a file containing the data up to 100,000
or perhaps 1 million.

The linear trend can be investigated.

I was thinking about doing this myself but I haven't got the time
right now.  I am not a tenured professor and I do not have an abundance
of free time (unfortunately).

 
All the four features above should hold for any base, not just 10.
There's really nothing special about base 10. The base can be chosen as
any positive real number. In fact, it would be nice to have the same
plot, but for number system in base e :-)
 

That is quite true -- for any integer base it will be the same.

For an irrational base, however, I cannot comment.

Correct me if I am wrong, but an irrational base has no practical
or even theoretical utility in expressing INTEGER quantities, and
INTEGER quantities are the basis for our counting system.

Sure, we can express PI as 1.0 in base PI but what does that
improve?