Tetration and p-adic

[JmsNxn]

Dear Ember Edison, that reference is an old one, you can find the most recent results here: https://arxiv.org/abs/2208.02622 (see Section 2 for the g-adic/p-adic stuff) and https://arxiv.org/abs/2210.07956

I would be glad if somebody here could manage to simplify the given results in terms of p-adic (for any given squarefree numeral system, maybe).

Thanks a lot, I'll try to understand it.

Hey, Ember. Remember that this paper is discovering a recursive pattern in the distribution of the digits \(^Na\); where upon this recursive pattern as \(N\to \infty\) repeats itself. And therefore we have something kind of p-adic. We have something like:

\[
^\infty a = \overline{(a_1a_2a_3...a_p)} A\\
\]

Where \(A\) is a fixed natural sequence of digits; as is \((a_1a_2a_3...a_p)\). But the latter continues on infinitely towards the left. Where, Marco's paper is shredding how to find \(a_j\) for all \(1 \le j \le p\).

Which just fucking smells like \(p\)-adic!  

Great job with your work, Marco! I've re read a bunch of your stuff. You're definitely on to something! I think there might be some clever trick that your missing. But still. Dope as fuck!

Regards, James