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Old 2021-08-02, 13:29   #1266
richs
 
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392^55 terminates P3 at i94.
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Old 2021-08-03, 07:43   #1267
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Quote:
Originally Posted by yoyo View Post
I go a base up to n^100 and a sequence up to composites of C139.
So e.g. for base 288 288^61, 288^67 and 288^68 are handled right now.

When I take a base, I take everything from n^1 to n^100, which has not finished and has a composite < C140.

I understand that your criteria make you handle sequences that are not taken into account by our project page.
If you handle base 288 with exponents > 60, it raises the question for me :

Do you think I should extend all bases < 1000 to exponent 70 on the project page ?
Please give me your opinions on this question, because the limit exponents I chose are not a rigorous choice.

For example for base 999, we have 999^70 which has 210 digits !
It's just to avoid nonsense.
I can't put 8128^100 on the page, because that number has 391 digits !
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Old 2021-08-03, 08:29   #1268
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Quote:
Originally Posted by sweety439 View Post
Conjectures:

* If n is odd, then 276^n never terminate.
* If n is even, then 276^n must terminate.

This happens for all bases.

Reminder :
- Sequences whose bases and exponents have the same parity usually terminate trivially (the only exception currently known : 29^15).
- Sequences whose bases and exponents do not have the same parity end very rarely.
- For bases that are doubles of squares, all sequences end trivially in general (no exception known at the moment).

This is due to a theorem that says that in a sequence, there is a change of parity only when a term is a perfect square or the double of a perfect square.
And in general, when we have odd terms in a sequence, it ends quickly.
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Old 2021-08-03, 08:51   #1269
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Quote:
Originally Posted by Happy5214 View Post
IMO bases which themselves are main project sequences (like the Lehmer five) should form a new category on the main page given their particular notability.

Honestly, I am against this idea.
Indeed, if Catalan's conjecture is true, then the sequences of the main project will all come out of the main project one day.
The placement of a base in this hypothetical new category would therefore be in no way final, unlike the placements of bases in all our other current categories.
But I agree that creating a category for the Open-End bases of the main project would facilitate the statistics !
Because, in the other hand, it is very interesting indeed to calculate the sequences of the bases in the main project.
I had already noticed that for the Lehmer five, non-trivial sequences ending seemed to be very rare.
But I think this must be a coincidence.
Otherwise, we would have a very curious conjecture !
It's a great idea to dig into this question !
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Old 2021-08-03, 09:01   #1270
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Quote:
Originally Posted by sweety439 View Post
The page has "Primorials", but does not have "Factorials", I try to take the factorials.

Also, I try the highly abundant numbers, since they are the numbers whose sigma function sets record, and sigma function is highly related to Aliquot sequences.

Besides, there are also interesting bases: 102 and 138, see https://oeis.org/A098009, they set record for the length of Aliquot sequences.

Finally, not only the Lehmer five, there are also other numbers less than 1000 which is conjectured to have an infinite, aperiodic, aliquot sequence: 306, 396, 696, 780, 828, 888, 996, which have the same trajectories as the Lehmer five.

Let me know if you manage to initialize bases with the minimum rules we set : for a given base, compute all sequences <120 digits that end trivially and <100 digits that are Open-End.
These are only the minimal rules, you can do more if you have big computational resources ;-)
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Old 2021-08-03, 09:44   #1271
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Quote:
Originally Posted by garambois View Post
Let me know if you manage to initialize bases with the minimum rules we set : for a given base, compute all sequences <120 digits that end trivially and <100 digits that are Open-End.
These are only the minimal rules, you can do more if you have big computational resources ;-)
OK, reserve base 120 (= 5!)
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Old 2021-08-03, 13:55   #1272
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Quote:
Originally Posted by garambois View Post
I understand that your criteria make you handle sequences that are not taken into account by our project page.
If you handle base 288 with exponents > 60, it raises the question for me :

Do you think I should extend all bases < 1000 to exponent 70 on the project page ?
Please give me your opinions on this question, because the limit exponents I chose are not a rigorous choice.

For example for base 999, we have 999^70 which has 210 digits !
It's just to avoid nonsense.
I can't put 8128^100 on the page, because that number has 391 digits !
You don't need to expand the exponent.
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Old 2021-08-03, 15:10   #1273
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Page updated.
Many thanks to all for your help !
Please let me know if you notice any errors.

Added bases : 14264, 14536, 15472 (C5 cycle completed !).
New bases reserved by yoyo : 39, 40, 44, 48, 50, 53, 62, 74, 162, 211, 722, 882.
Several terminated sequences of other bases with attribution.

I will be able to start doing the first data analysis tests of the project later this week...


Quote:
Originally Posted by yoyo View Post
You don't need to expand the exponent.
OK, Thank you for your answer.


Quote:
Originally Posted by sweety439 View Post
OK, reserve base 120 (= 5!)
Thanks !
The reservations on the page will be effective only when the base will be initialized.
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Old 2021-08-03, 18:07   #1274
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Looks like somebody might need more numbers to factor. I'll initialize bases 52, 54 & 55 next.
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Old 2021-08-03, 21:55   #1275
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392^57 terminates P42 at i27.

392^59 terminates P34 at i84.
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