mersenneforum.org (https://www.mersenneforum.org/index.php)
-   Aliquot Sequences (https://www.mersenneforum.org/forumdisplay.php?f=90)
-   -   Aliquot sequences that start on the integer powers n^i (https://www.mersenneforum.org/showthread.php?t=23612)

 Happy5214 2021-09-02 11:45

24^57:i1901 merges with 1134:i9.

I'm also done with 24^51, 24^53, and 24^55.

 RichD 2021-09-04 11:59

Base 57 can be added at the next update.

 garambois 2021-09-05 09:23

Page updated.
Many thanks to all for your help !
Please let me know if you notice any errors.

[B]For each of these bases, we have a sequence that ends in a cycle ![/B]

Still no non-trivial end of sequence for bases 276, 552, and 966.

 RichD 2021-09-05 14:52

Terminates:
57^45
57^73

 RichD 2021-09-08 20:39

Base 59 can be added at the next table update.

 RichD 2021-09-11 19:42

Base 60 should be ready at the next table update.

 garambois 2021-09-12 10:25

Thank you very much RichD.
I will add bases 59 and 60 in the next update which will be in the next week or two.

[B][U]What's new with regards to this project ?[/U][/B]

[B]The more new bases we have < 100 the better.[/B]
I'm actually thinking about a new way of analyzing the data that might be able to reveal a more complex law than the ones I've been looking for so far.
I don't know yet if my new idea will be successful, but I'm thinking of trying this new analysis around Christmas or during next spring.
I still have to think hard before I do it.
But this analysis can only be done on consecutive bases at first.
For now, we have all the bases exhaustively up to base 60.
In the future, I don't know yet if I will be able to extend the analysis up to base 1000, because we don't have all the bases < 1000 at all, there are holes.

But this new idea should not prevent us from continuing to make the calculations for the larger bases that will not be used directly in this new phase of the work !

 RichD 2021-09-12 13:39

Base 61 can be added at the next update.

 RichD 2021-09-15 21:54

Base 63 can be added at the next update.

Starting base 65. This is probably be my last table initialization for a bit while I catch up or other projects.

 RichD 2021-09-19 10:29

Base 65 can be added at the next update.

 garambois 2021-09-27 17:42

Page updated.
Many thanks to all for your help !

[B]Added bases : 59, 60, 61, 63, 65.[/B]
[B]Still no non-trivial end of sequence for bases 276, 552.[/B]
[B]On the other hand, for the base 966, we have the non-trivial sequence 966^31 which ends with the prime number 41 ![/B]

All times are UTC. The time now is 12:56.