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

yoyo 2021-12-06 06:45

I'll take bases 60, 61, 63, 65, 66 67, 68, 69.

EdH 2021-12-06 17:15

@garmbois: I'm looking at your plot data in [URL="https://www.mersenneforum.org/showpost.php?p=592117&postcount=1360"]post #1369[/URL] and wondering if I'm missing something. Some of your plots include the prime itself (e.g. 67 and 79 include (67, 1) and (79, 1) respectively), while 71 and 73 do not include themselves. From my limited viewing, the attached graphs appear to follow the posted data.

Obviously, I can enter these values (or remove them) for consistency myself for my "play," but, is there a reason they exist for some and not others, that I'm just missing?

garambois 2021-12-06 18:14

[QUOTE=yoyo;594551]I'll take bases 60, 61, 63, 65, 66 67, 68, 69.[/QUOTE]

Thank you very much.
This is fantastic, the calculations will really go much faster for these bases !

garambois 2021-12-06 18:25

[QUOTE=EdH;594583]@garmbois: I'm looking at your plot data in [URL="https://www.mersenneforum.org/showpost.php?p=592117&postcount=1360"]post #1369[/URL] and wondering if I'm missing something. Some of your plots include the prime itself (e.g. 67 and 79 include (67, 1) and (79, 1) respectively), while 71 and 73 do not include themselves. From my limited viewing, the attached graphs appear to follow the posted data.

Obviously, I can enter these values (or remove them) for consistency myself for my "play," but, is there a reason they exist for some and not others, that I'm just missing?[/QUOTE]


Congratulations for noticing this !

The explanation is simple : bases 67 and 79 are included in our project and bases 71 and 73 are not yet included in our project.
And when I wrote my analysis program, I only scanned the bases included in the project.
I judged that the amount of data for the other bases must be much too small to be of interest.
But maybe I was wrong ?
In any case, this was only the first attempt at this new analysis.
But to extend this kind of work, it will take a lot of time.
I don't really know how many bases are needed to notice something (all bases up to 100, 200, 1000 ?), or even if there is something to notice ?

EdH 2021-12-06 19:54

Thanks, Jean-Luc!

Is base 73 being worked by anyone? (I didn't see any mention in the thread.) If I don't hear an affirmative, I'll do some work there, but I don't know how active I will be.

garambois 2021-12-06 21:59

To my knowledge, no one is currently working on the 73 base.

EdH 2021-12-07 00:57

[QUOTE=garambois;594614]To my knowledge, no one is currently working on the 73 base.[/QUOTE]I'll work on it, but there are some larger exponents that are already finished that the db elves wouldn't have been involved in until near termination. The following exponents are all terminated:[code]73
61
47
41
37
35
33
31
29
27
25
23
21
19
17
15
14
13
12
11
10
9
7
5
4
3
2
1[/code]

RichD 2021-12-07 01:39

[QUOTE=EdH;594625]... but there are some larger exponents that are already finished that the db elves wouldn't have been involved in until near termination.[/QUOTE]

I remember starting on some bases, maybe 69-73, and only got to exponent 30s or 40s before abandoning my preliminary work. Whoever takes them won't have as much work to do to get them initialized.

EdH 2021-12-07 03:16

[QUOTE=RichD;594627]I remember starting on some bases, maybe 69-73, and only got to exponent 30s or 40s before abandoning my preliminary work. Whoever takes them won't have as much work to do to get them initialized.[/QUOTE]Thanks! Just so I'm not stepping on toes. . .

garambois 2021-12-20 11:39

Page updated.
Many thanks to all for your help !

[B]Added base : 69.[/B]
[B]Still no non-trivial end of sequence for bases 276, 552.[/B]
[B]New bases reserved for yoyo : 60, 61, 63, 65, 66, 67, 68, 69.
[/B]
Our project now has 112 bases and 10262 sequences.
There has been a lot of progress in the calculations for this update, as the yoyo statistics have been high the last two weeks :
31 sequences ended with one non-trivial (56^61).

:smile:

EdH 2021-12-26 16:55

Is anyone working base 70 or 71?


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