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

garambois 2020-08-15 08:17

@ yoyo :
Thanks a lot !
Just out of curiosity, are the calculations done by BOINC's yafu project ?


@ EdH :
OK.
So I'm going to focus using my tables on the case of the odd numbers you mention in post #364.

garambois 2020-08-15 08:21

I don't remember being so hesitant in my work on aliquot sequences. I've been running my analysis algorithms for over a week now. Then finally, I decided several times to modify them to make the results more accessible or to make other phenomena appear.
And I observe a lot of conjectures. I observe so many that it is difficult to see which ones are the most interesting. I don't even know how to present all this to you clearly. I am preparing a huge post with a selection of some of the most representative conjectures.
But I still need more time.
My dream is to find a general conjecture, which was my original goal.
For example, I dream of being able to relate occurrences of prime numbers for bases p and q (prime p and q) to occurrences of prime numbers for the base p*q.

yoyo 2020-08-15 08:24

[QUOTE=garambois;553747]@ yoyo :
Thanks a lot !
Just out of curiosity, are the calculations done by BOINC's yafu project ?
[/QUOTE]

Yes they are handled by BOINC's yafu project.

garambois 2020-08-15 10:00

[QUOTE=yoyo;553750]Yes they are handled by BOINC's yafu project.[/QUOTE]


WAOUH, thank you !!!


:tu:

RichD 2020-08-15 11:53

[QUOTE=EdH;553628]If I do any more, I'll just have to manually work them. But, as I mentioned, I'm probably nearing my boundary. If ECM doesn't factor them at least into the 16x area, I'm not inclined to run GNFS at that level right now.[/QUOTE]

I'm thinking if you can keep the first few terms locally then add the sequence to FDB once it drops below 200 digits. That requires a few extra steps but you could continue your analysis a bit further.

yoyo 2020-08-15 20:54

[QUOTE=yoyo;553680]I run some of the 3^i for i<=96. You should update them from time2time. No need to reserve them for me.[/QUOTE]

Update: I take all 3^i which have composites < C140.

garambois 2020-08-16 09:30

[QUOTE=EdH;553726]I was just tossing out a couple things that seemed of interest. I can't do more for a few days. If it's not valid, that's fine. I'll look at it more in a few days.[/QUOTE]


I just reread post #379 : OK, a is not an even number !
I misunderstood !
I'm sorry !
The conjecture seems to be true but a must be prime.
But I don't know how to prove it !

garambois 2020-08-16 09:34

[QUOTE=yoyo;553830]Update: I take all 3^i which have composites < C140.[/QUOTE]


OK, thank you.
For the next update, very soon, I'll reserve the orange cells of base 3 for you.
Is that right ?
For the name of the contributor, I put "YOY" ?

yoyo 2020-08-16 11:41

Ok, you can put YOY on it.

RichD 2020-08-16 12:16

You can remove my name from the colored cells (orange/green) in the n=30 table. I am done with them, so please release.

Happy5214 2020-08-17 13:01

I do not deserve any credit for any of the green [I]n[/I]=21 sequences, as I did no work on those. I don't know if you (Jean-Luc) did them or if they were done directly on FactorDB, but those shouldn't be attributed to me.


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