mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Aliquot Sequences

Reply
 
Thread Tools
Old 2021-08-04, 07:42   #1277
sweety439
 
sweety439's Avatar
 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

1011111010012 Posts
Default

Quote:
Originally Posted by garambois View Post
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).
I looked the Aliquot sequence of 29^15, this sequence is very interesting, although the first numbers are odd and these numbers decrease quickly, but the sequence reach an odd square number (265^2) and immediately merges with 18528.

I am curious of which number is the smallest odd number whose Aliquot sequence has not yet been fully determined? 1521 = 39^2 is the smallest odd number with long Aliquot sequence.

Edit: I have found it with my program, it is 3025 = 55^2

Last fiddled with by sweety439 on 2021-08-04 at 07:48
sweety439 is offline   Reply With Quote
Old 2021-08-04, 13:34   #1278
bur
 
bur's Avatar
 
Aug 2020
79*6581e-4;3*2539e-3

39810 Posts
Default

All odd bases with even exponent should switch to an even number with the second term. It would be interesting to see which odd number that isn't a square is of yet open ended.
bur is offline   Reply With Quote
Old 2021-08-04, 23:47   #1279
Happy5214
 
Happy5214's Avatar
 
"Alexander"
Nov 2008
The Alamo City

10111101102 Posts
Default

276 and 552 are initialized. 564 is next, where a non-trivial termination is already known (564^5). I'll see if there are any other notable sequences.
Happy5214 is offline   Reply With Quote
Old 2021-08-05, 04:21   #1280
sweety439
 
sweety439's Avatar
 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

57518 Posts
Default

Completed 120^7 at 265 bits (120^2 terminates at 36781, 120^4 terminates at 2643497, 120^6 terminates at 103078882663, 120^8 terminates at 381673, 120^3 and 120^5 merges with other sequences), I will stop only if the number is > 2^256

Now reserving 120^9
sweety439 is offline   Reply With Quote
Old 2021-08-05, 07:00   #1281
garambois
 
garambois's Avatar
 
"Garambois Jean-Luc"
Oct 2011
France

7×97 Posts
Default

Quote:
Originally Posted by RichD View Post
Looks like somebody might need more numbers to factor. I'll initialize bases 52, 54 & 55 next.
OK, many thanks.
Let me know as soon as I can add these bases to the page.


Quote:
Originally Posted by richs View Post
392^57 terminates P42 at i27.
392^59 terminates P34 at i84.
Many thanks.
This data will be taken into account in the next update.


Quote:
Originally Posted by Happy5214 View Post
276 and 552 are initialized. 564 is next, where a non-trivial termination is already known (564^5). I'll see if there are any other notable sequences.
Many thanks.
I will add these bases in the next update.


Quote:
Originally Posted by sweety439 View Post
Completed 120^7 at 265 bits (120^2 terminates at 36781, 120^4 terminates at 2643497, 120^6 terminates at 103078882663, 120^8 terminates at 381673, 120^3 and 120^5 merges with other sequences), I will stop only if the number is > 2^256
Now reserving 120^9
Many thanks.
It is not necessary to report all the steps in the initialization of the base 120.
Let me know when you have calculated all the trivial sequences (even powers) up to 120^56 and for the non-trivial (odd powers) up to 120^57.
OK for term size up to 2^256.
garambois is online now   Reply With Quote
Old 2021-08-05, 07:43   #1282
garambois
 
garambois's Avatar
 
"Garambois Jean-Luc"
Oct 2011
France

12478 Posts
Default

Quote:
Originally Posted by Happy5214 View Post
IMO just extend everything beyond base 100 to a fixed digit start value (200 digits maybe?) and leave it at that, whatever exponent that is for that base. That seems round but rigorous enough, though we lose the roundness of the exponent limits themselves.
Thank you for your answer.
We had worked this way at the beginning of the project, but at a 120 digit limit.
It was sometimes laborious, because we always had to go and look at the limit exponent we had to work with.
Especially for yoyo, which reserves bases by large packages.
So I simplified it by putting round numbers in stages for the limit exponents.
And that turned out to be more convenient.
Moreover, for the limit exponents, I tried to find a compromise so that the number of digits in the last sequence of a base is not too big.
I know that no one will calculate sequences of more than 160 digits, at least not until the distant future !
But if other contributors want me to adopt the old method again, I will : all limit exponents for a base calculated so that the first term of the sequence has 200 digits.
Current state of opinion :
- Alexander : limit exponent for each base calculated so that the first term of the last sequence of a base has 200 digits
- Yoyo : leave everything as it is now
- Myself : leave everything as it is now except for b bases such as 280<b<1000 : extend to exponent 70


Quote:
Originally Posted by Happy5214 View Post
That answer seems contradictory. You first say the category is a bad idea, and then you say it could be a good idea? I'm confused. The set of open sequences is pretty steady, especially those below 1e5 (comparing the count on Wikipedia from mid-2015 to today's from the Blue Page, we've only eliminated 7 over that span, and none below 1e4), so while the set is not final, it is stable enough for long-term inclusion.
You are right, the answer seems contradictory !
But I'm really reluctant to create a new category whose bases could then be removed.
But maybe I'm wrong ?
Again, let's make democracy work.
If other contributors give their opinion on the subject, we will make a decision based on the majority that will make it easier for as many people as possible, it seems fair.
Current state of opinion :
- Alexander : add a category including the Open-End sequences of the main project
- Myself : do not add it
On the other hand, if the calculations show that there are really special things happening for these bases, or on the contrary, that nothing is happening at all, this can also make us change our opinion...


Quote:
Originally Posted by Happy5214 View Post
Edit: Unrelated, the credit on 882^44 needs to be changed to me. That was included in https://www.mersenneforum.org/showpo...postcount=1253.
OK, got it.
Sorry, this will be fixed in the next update.
garambois is online now   Reply With Quote
Old 2021-08-05, 12:43   #1283
RichD
 
RichD's Avatar
 
Sep 2008
Kansas

344310 Posts
Default

Base 51 can be added at the next update.
RichD is offline   Reply With Quote
Old 2021-08-05, 13:55   #1284
EdH
 
EdH's Avatar
 
"Ed Hall"
Dec 2009
Adirondack Mtns

2·1,999 Posts
Default

Quote:
Originally Posted by sweety439 View Post
. . . 120^3 and 120^5 merges with other sequences . . .
Code:
120^3:i0 merges with 1728000:i0
120^5:i77 merges with 442560:i81
EdH is offline   Reply With Quote
Old 2021-08-05, 15:05   #1285
sweety439
 
sweety439's Avatar
 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3,049 Posts
Default

Quote:
Originally Posted by EdH View Post
Code:
120^3:i0 merges with 1728000:i0
120^5:i77 merges with 442560:i81
120^3 = 1728000
sweety439 is offline   Reply With Quote
Old 2021-08-05, 16:18   #1286
charybdis
 
charybdis's Avatar
 
Apr 2020

17·29 Posts
Default

Quote:
Originally Posted by sweety439 View Post
Completed 120^7 at 265 bits ... I will stop only if the number is > 2^256
Okay, maybe I shouldn't be the one to say this as I haven't taken part in this particular sub-project, but surely 256 bits (78 digits) is far lower than everyone else has been going? It took me 6 minutes on one core to reproduce the work you did on 120^7. If it took you much longer than this then there's probably something wrong with your setup.
charybdis is offline   Reply With Quote
Old 2021-08-05, 20:37   #1287
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

10011100000002 Posts
Default

Welcome to Sweety's idea of contributing work. More time is spent writing posts than computing.

Sweety- You don't need to tell us what happens to each sequence. Just tell us when you're done with the entire base, and the data will all be imported. Cofactors of C100 or terms of 120 digits are more reasonable bounds than 256 bits; Yafu's quadratic sieve is enough firepower for those bounds, so aliqueit can still run without extra interaction on your part. I hope it's not your goal to repeat your CRUS performance with Gary, computing so little that the admin ends up preferring that you hadn't joined at all.
VBCurtis is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Broken aliquot sequences fivemack FactorDB 46 2021-02-21 10:46
Broken aliquot sequences schickel FactorDB 18 2013-06-12 16:09
A new theorem about aliquot sequences garambois Aliquot Sequences 34 2012-06-10 21:53
poaching aliquot sequences... Andi47 FactorDB 21 2011-12-29 21:11
New article on aliquot sequences schickel mersennewiki 0 2008-12-30 07:07

All times are UTC. The time now is 21:18.


Sun Oct 17 21:18:47 UTC 2021 up 86 days, 15:47, 0 users, load averages: 1.34, 1.41, 1.49

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.