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

 garambois 2021-08-21 08:13

[QUOTE=yoyo;586074]I'll take bases 276, 552 and 966.[/QUOTE]
Reservation and update made for these 3 bases.
Thank you very much, I will follow the evolution of the calculations with great attention.

 garambois 2021-08-21 08:53

@bur and VBCurtis :

Thank you very much for your positive messages.
I think you are right and that we should see the project as you say.
All our calculations for this project will be at least as useful as others anyway, given the important role that integer powers play in number theory.
And I've said it all along : I didn't know if the data analyses would yield interesting results.
I was not intending to stop the project, but as you say, rather to take a break from data analysis.
If there is a general law to observe, it must be much more complicated than I could have imagined.
And if any of us were to find this law by observing the tables attached in my post #1328, then, we would be taking a giant step forward in the knowledge of aliquot sequences.
But maybe this law does not exist.
Or maybe we are missing some data. But what we are missing is rather larger exponents for each basis, that is my hunch. And we all know that it is impossible to increase the number of exponents for the bases.
But it is likely that in the future I will have to look at the data forgetting the original reason for creating the project.
There must be a lot of other interesting things to discover (or not !).

So let's get on with our calculations, all those who like it.
And when our intuition tells us it's time, maybe we'll look at the data again and notice some interesting things because of those calculations !

:smile:

 Happy5214 2021-08-21 09:08

I'm flattered, but 276^70 should be marked Anonymous. I didn't even explore above [I]i[/I]=60 for any of the Lehmer five bases. It was probably your page-generating script that finished it off.

I've never been in this project for the conjectures, to be honest (other than fixing up your webpage). For me, it's all about the sequences being easier to work on than the main project, and filling in gaps to make the tables more complete. Keep shooting for the stars! We never know we'll find.

 RichD 2021-08-21 12:07

Terminates:
54^70
54^72
55^73

 garambois 2021-08-22 16:06

[QUOTE=Happy5214;586173]I'm flattered, but 276^70 should be marked Anonymous. I didn't even explore above [I]i[/I]=60 for any of the Lehmer five bases. It was probably your page-generating script that finished it off.
[/QUOTE]
OK thanks.
Next update I'll put this sequence as calculated by an anonymous person.

[QUOTE=Happy5214;586173]Keep shooting for the stars! We never know we'll find.[/QUOTE]
You can trust me for that !

[QUOTE=RichD;586185]Terminates:
54^70
54^72
55^73[/QUOTE]
OK thanks.
This will be taken into account in the next update.

 RichD 2021-08-24 11:12

Terminates:
52^76
54^74
54^76
55^75

This concludes my work on these tables.

I'll start on bases 56, 57,59 and 60.

 unconnected 2021-08-27 09:37

79^89 terminates!
BTW, I'm working on base 79 (odd n) up to 101.

 garambois 2021-08-29 09:31

OK, I'm back from a few days of vacation.

[QUOTE=RichD;586397]Terminates:
52^76
54^74
54^76
55^75

This concludes my work on these tables.

I'll start on bases 56, 57,59 and 60.[/QUOTE]
Thank you very much for this work.
The finished sequences will be taken into account in the next update.
For the initializations of the new bases, excellent !
Let me know when I should add them to our page.

[QUOTE=unconnected;586639]79^89 terminates!
BTW, I'm working on base 79 (odd n) up to 101.[/QUOTE]
Thank you very much !
Reservations will be noted in the next update.
You want to do the calculations for the odd exponents up to 99, right (and not 101 which is not on the page ?) ?

 unconnected 2021-08-29 14:58

[QUOTE=garambois;586796]
You want to do the calculations for the odd exponents up to 99, right (and not 101 which is not on the page ?) ?[/QUOTE]
Yes.

 garambois 2021-08-29 15:44

WOW, OK, so good luck, because the calculations will be very long, a record for the project !
Several sequences exceed 170 digits !
79^93 and 79^99 will be formidable, as the terms have the factor 3.

 RichD 2021-08-31 22:25

Base 56 can be added at the next update.

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