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2021-08-19, 09:30   #1328
garambois

"Garambois Jean-Luc"
Oct 2011
France

12778 Posts

It is now 10 days since I launched the big scan of the project to analyze the data.
And I've been looking at the data from all angles for days.
I was even seeing numbers at night in my sleep !
And then : NOTHING !
While analyzing the data last year and again a few months ago, I had observed some remarkable phenomena that led to the 140 conjectures you know.
But these easily remarkable and "obvious" things had not been foreseen and had been observed by chance while I was looking for something else.

What exactly am I looking for ?

This project was originally created to try to see if a sequence which starts with a number which is an integer power of a number was more likely to belong to such or such "branch" of the infinite graph of aliquot sequences.
For a given base b and an integer a to find, I was looking to observe things like :
"Sequences of the type b ^ (k * a) end with the prime number p (or with the cycle c) for any integer k. "
I am well aware that it is highly unlikely that such a conjecture could be formulated, but I have not finished looking.
Perhaps there is a rule to be found which is more complicated to formulate than this example.
But for now, I can't see where to look, I have to take a break.
But maybe I also missed something obvious ?

So, in attached files, I put at your disposal my observation tables : perhaps you will see something there that escaped me ?
Perhaps you will also find a way to visualize the data differently than I do to reveal interesting things ?
Good luck to you in your observations of these 4 big tables.

When it comes to cycles that end sequences, we still don't have enough to be able to do statistics.
I manually noted the data on paper with a pencil to make my observations : NOTHING EITHER !

Later, I will again make observations in other directions, outside of the original idea of the project, to try to find something else entirely.
But I keep in mind that the holy grail of this project would be to succeed in predicting the end of an aliquot sequence without having to calculate all the terms.
I'm just assuming that this is easier to do for sequences that start with whole powers than for all sequences in general.

Do not hesitate if you have any comments, or even criticisms to make following this post.
Maybe I need someone to bring me to my senses...

;-)
Attached Files
 Data analysis of the n^i project.zip (193.4 KB, 32 views)