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Old 2022-09-18, 08:25   #1904
garambois
 
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I have good news :
All of Karsten's, Edwin's and my results match.
Our programs are good !
The only differences between our results come from the fact that we did not do our scans at the same time and that in the meantime sequences were added for some primes.

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Old 2022-09-18, 08:27   #1905
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Quote:
Originally Posted by RichD View Post
Reserving all prime bases below 350 for initialization. (311, 313, 317, 331, 337, 347, 349)

Base 317 can be added at the next update. I occasionally look ahead and perform some work on sequences but this one seemed to have more work than I would do part-time.
Many thanks RichD.
Base 317 will be added to the page next week.
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Old 2022-09-18, 08:54   #1906
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Quote:
Originally Posted by EdH View Post
Interestingly, 7420738134810^14 is still showing abundance at term 4. Most matched parity sequences turn deficient at term 1, don't they?
Sometimes I do work on the first terms of sequences and on the abundance of these first terms, as I exposed for example in post #921.
But these works are often limited by the non matching parity sequences for which we are only at index 1 !
Because interesting things happen between the index term 1 and 2.
For bases 3 and 5, we do not have this problem, but for base 6, the problem starts to appear with the sequences 6^189, 6^207 and 6^209.
For the sequences with non corresponding parity, it is therefore interesting to try to remove all these 1's and to have instead 2's or 3's, which allows to do interesting things.

Quote:
Originally Posted by EdH View Post
Are there any stats I can dig for from my end to supplement your work, Jean-Luc?
Thank you very much Edwin, but there are no new tracks emerging at this time.
I know there are a lot of people who occasionally follow this thread.
If any reader has an idea or question, please feel free to ask.
Any idea is interesting and can start us on a new track.
Don't be afraid to ask questions, even if you think it seems too trivial.
We can often come up with very interesting things with trivial questions.
And if the question is more complicated, don't hesitate either.
If I don't understand it, there will always be someone who does and it will give them ideas.
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Old 2022-09-18, 16:21   #1907
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Quote:
Originally Posted by garambois View Post
I have good news :
All of Karsten's, Edwin's and my results match.
Our programs are good !
The only differences between our results come from the fact that we did not do our scans at the same time and that in the meantime sequences were added for some primes.

Good news, indeed - thanks!
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Old 2022-09-18, 16:35   #1908
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Quote:
Originally Posted by garambois View Post
For the prime number 43, I can add some statistics that I had done a few years ago, thanks to my fundamental database on aliquot sequences.
But at that time, I only had the sequences up to 10,000,000 (today, 30,000,000, maybe I should make new statistics ?).
Beware, for these statistics, all sequences <10,000,000 that have a term that exceeds 10^50 are considered Open-End and so, here, we must underestimate the number of sequences that end with 43.
Here is what the statistics say.
Of the first 10,000,000 sequences that start with the integers from 1 to 10,000,000, there are :
- 666638 that end with the prime number 43.
- 456843 that end with the prime number 59.
- 437318 that end with the prime number 41.
I resurrected my seqinfo program and modified it to work with the current regina_file of 2-30M. (I'm not sure the status of Aillias' version.) Anyway, here is what it shows for that full set:
Code:
1242103 sequences found for 41
1893305 sequences found for 43
1298078 sequences found for 59
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Old 2022-09-19, 02:25   #1909
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I have initialized middle-sized to large opposite-parity exponents to a cofactor >= 110 digits for all bases 100 thru 195.

All bases in that range were affected with the exception of double-square base 162.

Also done were newly added bases 396 and 696.

Attached is a document of the specific affected sequences.

I'm continuing with this effort for bases < 100.
Attached Files
File Type: txt opposite-parity work bases 100-195,396,696.txt (900 Bytes, 15 views)
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Old 2022-09-19, 12:50   #1910
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Bases 311 and 313 can be added at the next update.
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Old 2022-09-19, 14:29   #1911
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I'll reserve 34^105
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Old 2022-09-19, 17:03   #1912
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I'll take bases 76, 78 and 79.
77 is reserved by Jean-Luc Garambois.

yoyo
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Old 2022-09-19, 18:02   #1913
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The new thread has been created and I realized a way to use a different post as the first, so I won't need to edit someone else's. The new thread is at Index 1 Sequence Work for the "n^i" Aliquot Project. I'll update the list from time to time with added bases and removed sequences.
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Old 2022-09-19, 19:34   #1914
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@Gary, RichD, richs, yoyo :
Thank you very much for your work, your reservations, your initializations.
All of this will be on the page when we next update it in less than a week.

@Edwin :
Thank you very much for starting the new sub-project thread to move the sequences from index 1 to a higher index !
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