mersenneforum.org Aliquot sequences that start on the integer powers n^i
 Register FAQ Search Today's Posts Mark Forums Read

2021-02-19, 17:57   #815
garambois

"Garambois Jean-Luc"
Oct 2011
France

26·32 Posts

Quote:
 Originally Posted by EdH Actually, it shows two: Code: Running base 47 from 1 through 75 . . . 47^4:i1 merges with 106080:i0 47^40:i1455 merges with 875060:i6 Run took 92 seconds. I will try to run it against the entire set of tables later today and make a list of any merges not already noted.

Thank you for all this, because it is a help that makes things easier for me !

A few days ago, I also realized that some mergers already noted on our project page could become obsolete.
Indeed, if one of our sequence n^i has merged with a sequence of the main project and that then, this sequence of the main project has merged with another smaller sequence of the main project, the fusion noted on our page then becomes false !
Periodically, I will therefore have to run your script which automatically detects the mergers and check them all, even those already noted on my project page !
This represents an additional amount of work !

2021-02-19, 18:43   #816
EdH

"Ed Hall"
Dec 2009

371410 Posts

Quote:
 Originally Posted by garambois I will follow your work closely if you share it with us here. At the moment, I'm having a hard time figuring out the usefulness of creating a list of the last occurrences of various digit size : C9 / C30 / C60 / C80. . .
I am also not thinking of a need for C9/C30/C60 ATM, but remember them being done in the past and the addition to (or removal from) my script is simple. I will be sharing my adventures with this thread, as I am hoping what I do is of benefit to the project, rather than just myself.
Quote:
 Originally Posted by garambois 1000 downloads of .elf in 2 hours : This is not at all what I experienced in April 2020. I had instead a speed of an .elf file in 60 seconds. So this is very good news, maybe factodb's server is much faster now. I will give it a try over the next week.
I do think this is a speedup since last year. At this point, I have d/led >11k sequences.

I am using the AllSeq.txt from the "Blue Page" and intend to check any changes from your 2020 file. Is there a better source (other than your 2020 file)?

Quote:
 Originally Posted by garambois There really isn't a lot of change in a year. Each year you have to delete the sequences that have ended or that have merged with a smaller one from the main project. These are the ones that are reported on the last pages of this topic : https://www.mersenneforum.org/showthread.php?t=11837
I already have a script that can run the entire set looking for terminations, once I have all the sequences. I also intend to have a script that will check the C80 file itself for merges. My hope is to cut down on the need for manual searches.

2021-02-19, 18:51   #817
EdH

"Ed Hall"
Dec 2009

2·3·619 Posts

Quote:
 Originally Posted by garambois Thank you for all this, because it is a help that makes things easier for me ! A few days ago, I also realized that some mergers already noted on our project page could become obsolete. Indeed, if one of our sequence n^i has merged with a sequence of the main project and that then, this sequence of the main project has merged with another smaller sequence of the main project, the fusion noted on our page then becomes false ! Periodically, I will therefore have to run your script which automatically detects the mergers and check them all, even those already noted on my project page ! This represents an additional amount of work !
I'm guessing there will still be some manual checking needed, to compare a new run of merges with those in the tables. I will see how involved it is when I have a complete list. I can already see that there will be quite a few merges to check, with all the tables we now have. The total run itself is plodding along rather slowly. It is only on base 14 right now. But, with the larger bases, there will be less sequences, so it should speed up near the end. Maybe I can add a method to compare what's on the page with what is in the run and flag any out-of-date merge info.

2021-02-19, 20:30   #818
garambois

"Garambois Jean-Luc"
Oct 2011
France

57610 Posts

Quote:
 Originally Posted by EdH I am also not thinking of a need for C9/C30/C60 ATM, but remember them being done in the past and the addition to (or removal from) my script is simple. I will be sharing my adventures with this thread, as I am hoping what I do is of benefit to the project, rather than just myself. I already have a script that can run the entire set looking for terminations, once I have all the sequences. I also intend to have a script that will check the C80 file itself for merges. My hope is to cut down on the need for manual searches.

Quote:
 Originally Posted by EdH I'm guessing there will still be some manual checking needed, to compare a new run of merges with those in the tables. I will see how involved it is when I have a complete list. I can already see that there will be quite a few merges to check, with all the tables we now have. The total run itself is plodding along rather slowly. It is only on base 14 right now. But, with the larger bases, there will be less sequences, so it should speed up near the end. Maybe I can add a method to compare what's on the page with what is in the run and flag any out-of-date merge info.

Thank you for all this information and for all the work.
I look forward to your results and conclusions !

2021-02-19, 20:33   #819
garambois

"Garambois Jean-Luc"
Oct 2011
France

26·32 Posts

Quote:
 Originally Posted by EdH I am using the AllSeq.txt from the "Blue Page" and intend to check any changes from your 2020 file. Is there a better source (other than your 2020 file)?

Personally, I don't know of any other source.

 2021-02-19, 23:22 #820 EdH     "Ed Hall" Dec 2009 Adirondack Mtns E8216 Posts Ok, I have some scripts that allow me to check the entire set of tables for sequences that merge. Then, they check to see if the merge is already listed in a table and provide a list of those already within the tables (found) and a list of those not already within the tables (missing). They then list those two sets: Code: These merges were already present: 3^10:i15 merges with 1134:i9 3^14:i2 merges with 158814:i544 3^28:i429 merges with 25968:i10 3^42:i418 merges with 186192:i15 3^48:i400 merges with 27450:i55 3^58:i1001 merges with 40092:i6 3^74:i1432 merges with 619200:i4 3^204:i1060 merges with 4788:i6 5^6:i1 merges with 3906:i0 5^8:i3 merges with 564:i12 5^14:i98 merges with 607386:i315 5^22:i265 merges with 660:i21 5^26:i229 merges with 1134:i9 5^28:i165 merges with 20208:i10 6^7:i9 merges with 95280:i20 6^67:i890 merges with 27860:i2 6^81:i703 merges with 388600:i7 7^10:i18 merges with 171040:i1 7^12:i153 merges with 121392:i168 7^20:i1345 merges with 660:i25 7^96:i1267 merges with 4788:i6 10^9:i24 merges with 31240:i2 10^19:i273 merges with 11408:i15 10^29:i450 merges with 14022:i19 10^31:i324 merges with 64980:i48 10^71:i831 merges with 42532:i2 10^129:i2229 merges with 2173380:i159 11^4:i1 merges with 1464:i0 11^10:i257 merges with 45792:i35 11^24:i2001 merges with 903872:i5 12^15:i294 merges with 3366:i2 12^19:i120 merges with 23324:i10 12^29:i790 merges with 1778224:i0 12^35:i380 merges with 3876:i5 12^43:i488 merges with 2484:i8 12^47:i1301 merges with 1374120:i189 13^14:i50 merges with 555300:i10 13^16:i660 merges with 14320:i25 13^30:i728 merges with 3876:i11 14^7:i21 merges with 2484:i9 14^13:i262 merges with 167748:i33 14^31:i1396 merges with 65208:i6 15^4:i3 merges with 3432:i69 15^8:i77 merges with 147150:i17 15^12:i3841 merges with 368688:i2 15^18:i98 merges with 81600:i354 15^28:i976 merges with 81084:i14 15^42:i819 merges with 3366:i2 17^4:i21 merges with 1632:i37 17^6:i1 merges with 967278:i4 19^14:i765 merges with 755460:i25 20^7:i60 merges with 7044:i129 20^9:i27 merges with 709900:i10 20^37:i1855 merges with 660:i25 21^4:i46 merges with 6552:i4 22^5:i19 merges with 86388:i4 22^29:i321 merges with 5208:i6 22^41:i1065 merges with 14676:i15 23^12:i144 merges with 78660:i2 23^44:i1830 merges with 7560:i251 24^17:i282 merges with 29022:i20 24^25:i329 merges with 620712:i514 26^15:i350 merges with 2360:i4 26^35:i503 merges with 87612:i4 26^55:i458 merges with 871000:i0 28^21:i4035 merges with 818880:i7 29^6:i51 merges with 2441868:i4 29^15:i37 merges with 18528:i0 30^43:i2207 merges with 39060:i2 31^4:i2 merges with 14100:i2 31^18:i241 merges with 25396:i984 33^8:i275 merges with 48024:i10 33^10:i94 merges with 1009656:i2 37^18:i1430 merges with 3366:i2 41^32:i386 merges with 271980:i46 79^52:i2041 merges with 660:i25 210^13:i320 merges with 50064:i101 284^3:i701 merges with 21432:i50 385^4:i403 merges with 903872:i5 385^6:i244 merges with 3876:i5 496^3:i168 merges with 22908:i1 770^3:i29 merges with 165876:i98 1155^4:i36 merges with 1290378:i273 1155^6:i112 merges with 25968:i10 2310^1:i0 merges with 1578:i3 30030^1:i0 merges with 22518:i3 30030^19:i841 merges with 41364:i4 510510^1:i4 merges with 425052:i7 These merges were not found: 15^88:i963 merges with 562032:i26 30^3:i0 merges with 27000:i0 37^6:i126 merges with 109920:i1275 37^8:i151 merges with 1632:i37 37^12:i1057 merges with 10824:i28 37^22:i519 merges with 1567300:i0 37^30:i1193 merges with 35856:i3 41^4:i66 merges with 36468:i17 47^4:i1 merges with 106080:i0 47^40:i1455 merges with 875060:i6 I did just a few spot checks and all "seemed" accurate, but please check them for validity. I will need to do more work on the scripts before I post them (possibly combining them into one), but I wanted to get the above to you for use for the next update. Edit: If a new merge has replaced an old merge, it should just show as listed in the "not found" group, since the index numbers will have been different. Last fiddled with by EdH on 2021-02-20 at 00:48 Reason: plural matching
 2021-02-20, 08:43 #821 garambois     "Garambois Jean-Luc" Oct 2011 France 10010000002 Posts WAOUH, WAOUH, WAOUH !!! But how did you manage to write such a program ? What a fantastic, wonderful tool ! I suspected that there were sequences which merged but which were not listed, like 15^88 ! A very big thank you for this work : "He removes a thorn from our foot" (We say that in French !). For 30^3, I knew about it ! But your program is beautifully written if it detected it. Indeed, 30^3 = 27000. It is therefore not a merger, it cannot merge with itself. Do you think I should note this fusion with himself on the project page ? Note that 30^3 is the only Open-End sequence that belongs to our project and to the main project at the same time. I already wanted to calculate it, but I don't have enough computing power right now.
2021-02-20, 15:00   #822
EdH

"Ed Hall"
Dec 2009

2·3·619 Posts

Quote:
 Originally Posted by garambois WAOUH, WAOUH, WAOUH !!! But how did you manage to write such a program ? What a fantastic, wonderful tool ! I suspected that there were sequences which merged but which were not listed, like 15^88 ! A very big thank you for this work : "He removes a thorn from our foot" (We say that in French !). For 30^3, I knew about it ! But your program is beautifully written if it detected it. Indeed, 30^3 = 27000. It is therefore not a merger, it cannot merge with itself. Do you think I should note this fusion with himself on the project page ? Note that 30^3 is the only Open-End sequence that belongs to our project and to the main project at the same time. I already wanted to calculate it, but I don't have enough computing power right now.
I totally glossed over the i0=i0. Very unobservant of me. It isn't something to note. Rather I wonder if I should provide a filter to remove it from future listings. I probably won't since we are aware of it, and as you say, it isn't a merger, just a hit with the 80 digit file.

Speaking of the 80 digit file, I'm at 20k of the downloads. I ran my termination detection across those I already had at the time, with no hits, but if the AllSeq.txt from the Blue Page is anything near current, I shouldn't get any hits at this time. That may not be true of merges within the AllSeq.txt. If nothing has changed in merge detection for the Blue Page, it is quite possible (maybe even probable) that there will be undetected merges. That's one of the next scripts I'll be working on.

I still need to find a way to compare last lines, so I can limit updates to those sequences that have changed. Then I can do full set updates in a much more timely manner. I'm actually going to be doing that with my table sets, as well. In the past, I've been updating the full set by downloading the entire .elf for any that weren't terminated. But, the number of tables (and, therefore sequences) has grown considerably since then. As soon as I do another full update of the table .elfs, I'll work on an 80 digit file for them, too.

My "farm" is quite tied up with a larger job than I expected, or should have tried. It may well be into next month before I can even free the bulk of the machines and then my main machine will be busy for a long time with the LA, if I'm able to actually do it. Otherwise, I could run the c151 for 27000. I wonder, since it is an open sequence of the main project, if we might make a case for it to become a Team Project like 276, 3408, 3366 and 4788. All of those mentioned are at uncomfortably high composites. Maybe we could make a case for working this one, in that it is the only known open-ended sequence of its type and would offer some smaller composites for those interested in the Team Projects, but turned away by the sizes.

Edit: I was thinking of a different sequence. Please disregard the struck-out text. I'll go back into seclusion now (at least for a while). The one I was confusing with 27000 is 18528 which is the merge for 29^15, which was expected to terminate in a manner consistent with all the odd powered base 29 sequences. In light of that, would it be of interest to try for a Team Effort for that main project sequence?

Last fiddled with by EdH on 2021-02-20 at 16:38

2021-02-20, 23:29   #823
EdH

"Ed Hall"
Dec 2009

E8216 Posts

Let's see if I can redeem myself a little from that last oops. . .

I have attached a list of the C80s for all the open sequences represented in all the tables. Additionally, I found several merges within the tables:
Code:
5^26:i221 merges with 3^10:i7

3^204:i1053 merges with 7^96:i1260

37^18:i1428 merges with 12^15:i292
15^42:i810 merges with 12^15:i285

13^30:i728 merges with 385^6:i250
12^35:i371 merges with 385^6:i235

12^43:i489 merges with 14^7:i21

37^8:i150 merges with 17^4:i20

7^20:i1345 merges with 5^22:i269
20^37:i1855 merges with 5^22:i269
79^52:i2041 merges with 5^22:i269

11^24:i1993 merges with 385^4:i395

1155^6:i100 merges with 3^28:i428
As can be seen, three other sequences merge with 5^22:i269. I did not run down the merges between those three. There are also a couple others with multiple merges.

I think I may be taking a break. This last endeavor took a lot more manual intervention than expected. . .
Attached Files
 tablesC80list.txt (89.0 KB, 19 views)

 2021-02-21, 01:57 #824 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 72028 Posts I've attached a new C80 list. I believe it has 51 fewer sequences than the 2020 list. All are unique and open-ended. I did not add a preface to the list. Feel free to make full use of it. Of note, the Blue Page provided one sequence (1750944) in its AllSeq.txt which has not yet reached 80 digits. All the rest seemed to be what was expected. Note: The outdated list was removed from this post and a new one can be found in post #848. Last fiddled with by EdH on 2021-02-21 at 22:00
 2021-02-21, 03:14 #825 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 1110100000102 Posts 578^46 has turned green.

 Similar Threads Thread Thread Starter Forum Replies Last Post fivemack FactorDB 46 2021-02-21 10:46 schickel FactorDB 18 2013-06-12 16:09 garambois Aliquot Sequences 34 2012-06-10 21:53 Andi47 FactorDB 21 2011-12-29 21:11 schickel mersennewiki 0 2008-12-30 07:07

All times are UTC. The time now is 16:35.

Wed May 12 16:35:37 UTC 2021 up 34 days, 11:16, 1 user, load averages: 4.21, 3.73, 3.47