Aliquot sequences that start on the integer powers n^i - Page 81

garambois · 2021-02-26, 08:17

Quote:

Originally Posted by yoyo

Here here, here, I take base 45, 75 and 231.

Please I'm sorry to bother you again with the same issue.
But I'm starting to put things together for the next update.
However, I cannot find the bases 45, 75 and 231 in this folder :
https://yafu.myfirewall.org/yafu/download/ali/y/
Indeed, I do not know up to which exponent you carry out the calculations for these bases.
Is that the exponent 100 ?
Sorry, I probably misunderstood something !

garambois · 2021-02-26, 08:19

Quote:

Originally Posted by EdH

I might have mentioned a couple of these before, but basically, all cells of bases 450 and 578 through exponent 50 are now green (terminated).

OK, many thanks !

garambois · 2021-02-26, 13:26

Quote:

Originally Posted by garambois

Yes, I am planning to update the C80 digit file very quickly. But the scan of the 27,000 sequences takes several days (21 days !).
I will also create a C80 file for all the Open End sequences in our project, as advertised here :
https://www.mersenneforum.org/showth...12&page=65#714
Please keep me posted if you are doing any work in this direction as well !

It is not possible to create a C80 file for the sequences of our project.
I don't know how to tackle the problem.
This is not possible for all sequences, because many of our sequences start to grow from the beginning and their starting number is already over 80 digits.
The solution would be to make a C100 or C120 list, but the problem remains the same for several sequences.
Then a C130 list ?
There, the problem is the opposite since many sequences of our project did not reach 130 digits. We stopped the calculations before.
So I don't know how to create a reliable tool to spot the sequences that would merge with those in our project.
Perhaps one should limit oneself to a C80 list for the sequences which have them, because anyway, I do not know of an example of a merger above 80 digits !

yoyo · 2021-02-26, 16:25

Quote:

Originally Posted by garambois

Please I'm sorry to bother you again with the same issue.
But I'm starting to put things together for the next update.
However, I cannot find the bases 45, 75 and 231 in this folder :
https://yafu.myfirewall.org/yafu/download/ali/y/
Indeed, I do not know up to which exponent you carry out the calculations for these bases.
Is that the exponent 100 ?
Sorry, I probably misunderstood something !

I didn't copied the new ones to this folder. But I start all bases up to exponent 100.

garambois · 2021-02-26, 17:02

OK, thank you !

Happy5214 · 2021-02-26, 23:35

Quote:

Originally Posted by garambois

It is not possible to create a C80 file for the sequences of our project.
I don't know how to tackle the problem.
This is not possible for all sequences, because many of our sequences start to grow from the beginning and their starting number is already over 80 digits.
The solution would be to make a C100 or C120 list, but the problem remains the same for several sequences.
Then a C130 list ?
There, the problem is the opposite since many sequences of our project did not reach 130 digits. We stopped the calculations before.
So I don't know how to create a reliable tool to spot the sequences that would merge with those in our project.
Perhaps one should limit oneself to a C80 list for the sequences which have them, because anyway, I do not know of an example of a merger above 80 digits !

If the point is to detect merges, just stick to the C80 file and the sequences that actually have 80-digit terms.

garambois · 2021-02-27, 17:36

Quote:

Originally Posted by Happy5214

If the point is to detect merges, just stick to the C80 file and the sequences that actually have 80-digit terms.

I don't know yet what I'll do, or if I'll publish a list of C80s for our project. I will see later if this concerns a few or a lot of sequences in the project.

But now I'm focusing on some new conjectures. I still have to wait for the end of several calculations to be more certain about these conjectures that I will present to you during next week.

RichD · 2021-02-27, 17:40

Please include bases 43 & 47 in the next update. There are some/many advances.

garambois · 2021-02-27, 19:40

Yes of course, many thanks !

Happy5214 · 2021-02-28, 07:02

I terminated another yoyo sequence, 3^90, thus connecting all of the green sequences in the base 3 table.

garambois · 2021-02-28, 10:12

Congrats !
Another non-trivial end of a sequence !

Ah, if we could have a second sequence which ends with a cycle for base 3, that would give us important information !
But it is now extremely unlikely ...

Reminder : we are always looking for a base which is not a perfect number and which would have sequences which end with cycles of different lengths.
It can only be a coincidence that it only happens with perfect bases !

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2021-02-26, 17:02	#885
garambois "Garambois Jean-Luc" Oct 2011 France 226₁₆ Posts	OK, thank you !

2021-02-27, 17:40	#888
RichD Sep 2008 Kansas 6363₈ Posts	Please include bases 43 & 47 in the next update. There are some/many advances.

2021-02-27, 19:40	#889
garambois "Garambois Jean-Luc" Oct 2011 France 2×5²×11 Posts	Yes of course, many thanks !

2021-02-28, 07:02	#890
Happy5214 "Alexander" Nov 2008 The Alamo City 1000111000₂ Posts	I terminated another yoyo sequence, 3^90, thus connecting all of the green sequences in the base 3 table.

2021-02-28, 10:12	#891
garambois "Garambois Jean-Luc" Oct 2011 France 1046₈ Posts	Congrats ! Another non-trivial end of a sequence ! Ah, if we could have a second sequence which ends with a cycle for base 3, that would give us important information ! But it is now extremely unlikely ... Reminder : we are always looking for a base which is not a perfect number and which would have sequences which end with cycles of different lengths. It can only be a coincidence that it only happens with perfect bases !