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

RichD 2022-11-21 11:30

Bases 401 & 409 can be added at the next update.
That is all the time I have at the moment.

garambois 2022-11-23 17:17

Page updated.
Thanks to all for your help.

[B]Added bases : 401, 409, 47616.[/B]
[B]Updates of some bases and some corrections made.[/B]

gd_barnes 2022-11-26 02:42

I have completed testing of new bases 401, 409, and 47616 all open sequences to >= 120 digits.

401^8 is an interesting one. It dropped all the way down to a value of 3086468 at index 1061 and 5 total indexes had values of < 4000000, yet it did not merge with the main project. Very surprising.

garambois 2022-11-27 08:59

If anyone has good computing power, I would be very interested in the opposite parity sequences for bases 103 and 313.
This is a work on sequences that end in cycles.
For base 313, there are several opposite parity sequences that look like they could easily go downdriver.

If no one can do these calculations to get these sequences to at least 120 digits, I will reserve them in a few days, but it will take weeks for me.

gd_barnes 2022-11-27 10:47

[QUOTE=garambois;618547]If anyone has good computing power, I would be very interested in the opposite parity sequences for bases 103 and 313.
This is a work on sequences that end in cycles.
For base 313, there are several opposite parity sequences that look like they could easily go downdriver.

If no one can do these calculations to get these sequences to at least 120 digits, I will reserve them in a few days, but it will take weeks for me.[/QUOTE]

I'll reserve base 313 for the opposite-parity sequences that are at < 120 digits and take them to >= 120 digits. I'll start on it with 2 machines within ~2 days. Once started, it would take ~3 days.

I am working currently on testing all sequences for bases 300 to 350 to >= 120 digits. I have 4 machines working on it full time. Base 349 is done, 2 machines are working on base 347 that should complete in ~1-2 days, and there is some work done on bases 337 and 331 that have 1 machine each working on.

After the 2 machines finish base 347 within the next couple of days, I'll have them do base 313 next.

Check back with me before you reserve base 103. I may decide to take it up after base 313.

All of the bases in the 300s have ~14-20 sequences to be worked to >= 120 digits. Base 103 has 24 sequences so it's going to be a bigger effort. I may decide to put 3-4 machines on it at once.

garambois 2022-11-27 12:21

Thank you very much Gary, this is fantastic !
Now let's see if an additional sequence will end in a cycle for one of these two bases.
For base 313, for example, it is quite curious that the two sequences that end in cycles both end in the cycle C2 = (1184,1210).
But this is certainly a coincidence !

For a base that is a prime number, all sequences that end in a cycle end in a cycle of the same length with the data we have so far.
We have not yet found any exceptions.

gd_barnes 2022-11-28 00:53

Ed is going to run base 103 to >= 120 digits.

That works well. It would have been ~5-7 days before I started on it.

garambois 2022-11-28 16:55

Thank you very much for your help !

garambois 2022-11-30 18:37

Small update done on the page.
Thanks to all for your help.

[B]4 errors pointed out by Karsten corrected, thanks to him.[/B]
[B]Bases 103, 313 and 47616 updated, thanks to Gary and Edwin.[/B]

I really would have bet that we would have sequence endings for base 313, even an ending on a cycle !

EdH 2022-11-30 18:55

I've hit several downdrivers, but no terminations. The downdrivers and some power glitches have really slowed my machines down.

I'm actaully watching a downdriver right now in the c7x range. . .

RichD 2022-11-30 23:52

As I have time.

Bases 419 & 421 can be added at the next update.


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