mersenneforum.org Aliquot sequences that start on the integer powers n^i
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2021-06-26, 08:21   #1189
garambois

"Garambois Jean-Luc"
Oct 2011
France

3·227 Posts

Quote:
 Originally Posted by Happy5214 I don't mean to speak on behalf of Jean-Luc, but my understanding is that the current computational priorities are initializing new bases < 100 (which I'm doing) and terminating trivial sequences, with a side subproject of initializing bases belonging to the 5- and 28-cycles (which I've also participated in). yafu@home (yoyo) handles most of the cycle advancement here, but only to a certain limit. As for my progress (to avoid making two posts), I'm probably going to start base 48 Saturday (it's 2 AM here, but it feels like Friday still). I'm not reserving the cycle sequences at this time.
I would have answered exactly the same !
There is also the possibility of initializing the bases 648, 722 and 800 which are doubles of the squares between 578 and 882 that we already have on our page at the moment.
For these bases, all sequences end trivially.
And these are certainly the bases that are most likely to give us sequence endings on cycles.

Quote:
 Originally Posted by bur Ok, then I'll finish term 26 of 79^76 and then begin with base 53 which seems the smallest prime base not initialized yet. A lot of the smaller exponents for 53^n are already terminated in factordb.
Perfect, many thanks !
Let me know when base 53 is ready to be put on the page.

Quote:
 Originally Posted by bur Is there any advice on initializing or should I just use aliqueit ?
I'm sorry, but I personally don't use aliqueit so I can't answer this question.
I use my own program written with Olivier Huber and Paul Zimmermann.
This program uses several factorization methods including at the end an ECM method and CADO-NFS.
It is written in python and I change the parameters according to the type of sequences I calculate.
Sequences of the form n^i for example do not behave like sequences of the form 2^5*3^3*5*7*n on which I also work (growth at each iteration of a factor at least equal to 3).

2021-06-26, 10:38   #1190
Happy5214

"Alexander"
Nov 2008
The Alamo City

3·11·23 Posts

Quote:
 Originally Posted by bur Is there any advice on initializing or should I just use aliqueit?
I just use a queuing system to call aliqueit with the -y flag, which simply calls yafu on each term after some TF and rho. The system also handles the configuration, which I set to a digit limit of 100 for the non-trivial sequences and a cofactor digit limit of 120 for the trivial ones (both through aliqueit parameters).

2021-06-26, 12:51   #1191
EdH

"Ed Hall"
Dec 2009

33·149 Posts

Quote:
 Originally Posted by bur . . . Is there any advice on initializing or should I just use aliqueit?
Aliqueit is fine (as I see Happy5214 has mentioned). The only downsides are that it won't update the db until you tell it to and it won't detect merges until then. (Merges are actually quite rare, anyway.) As Happy5214 mentioned, there are some options for term and cofactor lengths.

There's also a Perl script by yoyo that works directly with the db, so it updates each term. There's a thread about it. There is an option for term length, but not for cofactor length. It relies on YAFU for all the factoring.

2021-06-26, 13:21   #1192
Happy5214

"Alexander"
Nov 2008
The Alamo City

3×11×23 Posts

Quote:
 Originally Posted by EdH [...]it won't detect merges until then. (Merges are actually quite rare, anyway.)[...]
@bur: As a general rule, if the sequence gets below 10 digits or so, you may want to stop it, upload, and check FactorDB to see if it merged. (You'll have to check the console scrollback after the downdriver run, once things have slowed down a bit.) Most (almost all?) merges happen below 15 digits, so don't bother checking if it doesn't get that far down.

2021-06-26, 14:11   #1193
EdH

"Ed Hall"
Dec 2009

33×149 Posts

Quote:
 Originally Posted by Happy5214 @bur: As a general rule, if the sequence gets below 10 digits or so, you may want to stop it, upload, and check FactorDB to see if it merged. (You'll have to check the console scrollback after the downdriver run, once things have slowed down a bit.) Most (almost all?) merges happen below 15 digits, so don't bother checking if it doesn't get that far down.
What he said! But, I would also add that i wouldn't worry about checking until the sequence started growing again and slowed down in its steps.

Just to mention, you can open a second terminal and have Aliqueit do an upload without disturbing your main process. just use "-s <term#>" in your command line, with <term#> being 0 or the last current term in the db.

2021-06-27, 06:20   #1194
bur

Aug 2020
79*6581e-4;3*2539e-3

13·31 Posts

Aliqueit shows a "merges with earlier sequence" for each 53^n because the i1 term is always smaller than i0.

How should that be handled? Technically it does merge after all...

And a question about the process, aliqueit doesn't accept b^n as input, so do I really need alq_123...789.elf files with more than 100 characters or is there a better way?

Quote:
 Originally Posted by garambois I use my own program written with Olivier Huber and Paul Zimmermann. This program uses several factorization methods including at the end an ECM method and CADO-NFS. It is written in python and I change the parameters according to the type of sequences I calculate.
That sounds good, I found cado to be faster than msieve. Is that script publicly avilable?

Last fiddled with by bur on 2021-06-27 at 06:22

 2021-06-27, 07:45 #1195 garambois     "Garambois Jean-Luc" Oct 2011 France 3·227 Posts Page updated. Many thanks to all for your help. Added base : 44. I have changed the display of the Cycles in the "Navigation" part, so that we can see the complete and incomplete cycles.
2021-06-27, 12:42   #1196
EdH

"Ed Hall"
Dec 2009

402310 Posts

Quote:
 Originally Posted by bur Aliqueit shows a "merges with earlier sequence" for each 53^n because the i1 term is always smaller than i0. How should that be handled? Technically it does merge after all...
In aliqueit.ini, there is a line for detecting merges. change that to false:
Code:
//Stop if sequence merges with an earlier sequence?
detect_merge = false
Quote:
 Originally Posted by bur And a question about the process, aliqueit doesn't accept b^n as input, so do I really need alq_123...789.elf files with more than 100 characters or is there a better way?
You'll need the entire expanded composite for Aliqueit.

2021-06-27, 16:19   #1197
bur

Aug 2020
79*6581e-4;3*2539e-3

13×31 Posts

Quote:
 In aliqueit.ini, there is a line for detecting merges. change that to false:
I did that, but won't aliquoeit cease to detect merges altogether? How do I detect merges in that case? From what you wrote it seemed to me aliqueit would be doing that job.

2021-06-27, 18:47   #1198
EdH

"Ed Hall"
Dec 2009

33·149 Posts

Quote:
 Originally Posted by bur I did that, but won't aliquoeit cease to detect merges altogether? How do I detect merges in that case? From what you wrote it seemed to me aliqueit would be doing that job.
To Aliqueit, detecting a merge means the current term has fallen below the value of the original term. This works great for a sequence that begins with a small(ish) <10^7 number. But the n^i project starts at all variety of lengths. For this project a merge is usually indicated by the db displaying more lines than we gave it from our work. At that point we need to check for merges in a different manner. garambois has a file that contains the last 80 digit terms for all the open-ended sequences from the main Aliquot project. This file is used to find with what sequence and at which point the merge occurs. I provided a program in post #794 to help with that search.

Last fiddled with by EdH on 2021-06-27 at 18:48

 2021-06-27, 18:57 #1199 bur     Aug 2020 79*6581e-4;3*2539e-3 1100100112 Posts Ok thanks. 53^30 terminated so it definitely merges with some lower sequence and a few others went below 15 digits. But I'll continue finishing the sequences to 110 digits and then check for merges in one go. Might waste some computation time on select occasions, but is easier for me.

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