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Old 2020-08-12, 07:59   #406
garambois's Avatar
Oct 2011

22×3×29 Posts

Originally Posted by garambois View Post
The first array is finished.
You can see it as an attachment (.pdf version).

It is difficult to draw definite conclusions because we don't have a lot of sequences that end for large bases after all.
But what I was hoping for is not happening.
Sequences that start on integer powers seem to generally end with the same probability on the same prime numbers as all of the sequences.
So there's no obvious conjecture to be made... yet.

I will redo all this work by considering all the prime numbers that appear in all the terms of the sequences, as described above.
I will also publish the final array here.

If anyone has any questions or notices things that I wouldn't have seen when looking at this array, please feel free to express them here !

As announced in post #337 cited above, here is the attached pdf which shows the occurrences of prime numbers <1000 for all the bases. Here, we consider globally all the terms of all the sequences for a base. It is rather the prime numbers 31 and 127 which are distinguished from the others. But this is understandable since they are the prime numbers of the drivers...

I didn't fill in the column called "integers from 1 to 10^4".
Downloading all the complete sequences on db would have been much too laborious !

That said, it would certainly be extremely interesting to redo for all the integers all this prime number analysis work that we did for only the integer powers. Some very interesting things would certainly appear. I am talking about all the works, and not only those shown on this pdf and the pdf of post #337 (works also showing multiple apparitions of a prime number in a single sequence by indicating the indexes of appearance). Now that the programs are written, it would be easy to do the analyses for all the integers. The problem is the downloading of all the terms of all the sequences...
Attached Files
File Type: pdf Aliquot sequences n^i all primes.pdf (54.3 KB, 12 views)
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