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-   -   Aliquot sequences that start on the integer powers n^i (https://www.mersenneforum.org/showthread.php?t=23612)

 garambois 2018-08-28 13:27

Aliquot sequences that start on the integer powers n^i

On my website, I wrote a page that summarizes my work on aliquot sequences starting on integer powers n^i. This page summarizes the results and reservations for each aliquot sequences one has chosen to calculate.

[URL="http://www.aliquotes.com/aliquotes_puissances_entieres.html"]See this page.[/URL]

If someone in this forum also wants to calculate these aliquot sequences with me, he can indicate it to me here and I note his name in the cells of my page to reserve him the integer powers of his choice.
He will then have to enter the results into factordb and let me know so that I can fill and color the cells of the array as appropriate.

Note : For open-end aliquot sequences, I stop at 10^120 (orange color cells).

Edit: The following link will take you to a regularly updated page of conjectures that have been formed based on this project:

[URL="http://www.aliquotes.com/conjectures_mersenneforum.html"]Conjectures related to aliquot sequences starting on integer powers [I]n^i[/I][/URL]

 LaurV 2018-08-29 15:38

I am (occasionally) working on 6^n, the progress for the larger seq is due to me, in the past.

 garambois 2018-08-30 12:52

OK LaurV,

Do you remember for which i values you calculated the aliquot sequences of 6^i ?
So I can add your name instead of "A" (Anonymous) in the array.

 LaurV 2018-08-30 17:56

Below 20 (and inclusive) the only sequences which do not terminate are 6^(7, 9, 11, 15, 19).

They are all at the point where I left them, except for few terms of 6^15 added by the elves where the last cofactor was under 110 digits. I work on 10077696 (6^9), and I reserved 95280 years ago, when 279936 (6^7) merged with it. I brought it to 148 digits (currently with a C140 cofactor, I still have it reserved, but not in priority list due to the 2^4*31 driver).

Interesting that even powers (including higher, to 30 or 50, can't remember) all terminate, some in very large primes. Also, odd powers between 21 and 31 were left after C>100, and were advanced a bit by the DB elves.

 garambois 2018-08-30 21:42

[QUOTE=LaurV;494959]Below 20 (and inclusive) the only sequences which do not terminate are 6^(7, 9, 11, 15, 19).

They are all at the point where I left them, except for few terms of 6^15 added by the elves where the last cofactor was under 110 digits. I work on 10077696 (6^9), and I reserved 95280 years ago, when 279936 (6^7) merged with it. I brought it to 148 digits (currently with a C140 cofactor, I still have it reserved, but not in priority list due to the 2^4*31 driver).

[/QUOTE]

OK, I wrote your name on [URL="http://www.aliquotes.com/aliquotes_puissances_entieres.html"]the page[/URL].

[QUOTE=LaurV;494959]

Interesting that even powers (including higher, to 30 or 50, can't remember) all terminate, some in very large primes. Also, odd powers between 21 and 31 were left after C>100, and were advanced a bit by the DB elves.[/QUOTE]

Yes, If n is even and if and only if n takes the form n=m^2 or n=2*m^2, then sigma(n)-n will be odd.
If n is odd and if and only if n takes the form n=m^2, then sigma(n)-n will be even.

[URL="http://www.aliquotes.com/changement_parite.pdf"]See the proof[/URL], but sorry, in french.

So, because n=6^i always is even, and n takes the form n=m^2 only when i is even, then, sigma(n)-n will be odd and the aliquot sequence will go down. If i is odd, then we will probabily have an Open-End aliquot sequence.

If for example, we take n=5^i which always is odd, when i is even then n takes the form n=m^2, so sigma(n)-n will be even, so the aliquot sequence will probabily be Open-End.

If for example, we take n=2^i which always takes the form m^2 (if i is even) or the form 2 * m^2 (if i is odd), then, sigma(n)-n will always be odd, so the aliquot sequence will probabily always go down.

I would like to find one i with 2^i an open-end sequence, but I haven't found such an aliquot sequence yet.

 garambois 2018-09-19 19:40

Thanks to Karsten Bonath for completely redesigning my [URL="http://www.aliquotes.com/aliquotes_puissances_entieres.html"]calculation tracking web page[/URL].

The new page is much more readable and allows immediate access to the data on FactorDB with a simple click.

For the moment, only some aliquots sequences for n=2^i, 3^i, 6^i and 11^i are reserved.

 RichD 2018-09-19 23:22

AS 11^56 terminates.
Edit: AS 11^58 terminates.

 RichD 2018-09-20 01:19

AS 10^108 terminates.
AS 10^104 terminates, not by me.

 wpolly 2018-09-21 00:03

6^77 terminates.

 garambois 2018-09-23 20:26

OK,

RichD and wpolly, page updated.
Thank you for your help !

 RichD 2018-09-25 14:04

10^106 terminates with a prime - 91909.

 kar_bon 2018-09-25 14:54

Terminations:
5^169
7^129
7^135

 RichD 2018-09-25 21:19

Added several hundred steps to 11^68 until it acquired 2^2 * 7 - again.

 RichD 2018-09-26 22:52

10^112 terminates.

 kar_bon 2018-09-28 06:52

6^81:i703 merges with 388600:i7

 RichD 2018-09-29 09:53

10^114 terminates.

 garambois 2018-09-29 12:57

OK, Updated.
Thank you very much.

 RichD 2018-10-06 09:41

11^80 terminates.

 garambois 2018-10-07 15:38

OK, Updated.
Thank you very much.

 kar_bon 2018-10-08 22:34

6^140 terminates

 kar_bon 2018-10-09 19:23

6^142 terminates

 kar_bon 2018-10-09 21:29

6^144 terminates

 sweety439 2018-10-12 17:47

[QUOTE=garambois;494797]On my website, I wrote a page that summarizes my work on aliquot sequences starting on integer powers n^i. This page summarizes the results and reservations for each aliquot sequences one has chosen to calculate.

[URL="http://www.aliquotes.com/aliquotes_puissances_entieres.html"]See this page.[/URL]

If someone in this forum also wants to calculate these aliquot sequences with me, he can indicate it to me here and I note his name in the cells of my page to reserve him the integer powers of his choice.
He will then have to enter the results into factordb and let me know so that I can fill and color the cells of the array as appropriate.

Note : For open-end aliquot sequences, I stop at 10^120 (orange color cells).[/QUOTE]

Why stop at 11? I suggest stop at 24

Now, I am running 12 and 13

(also, I have run 2^n-1 and 2^n+1 for n<=64)

 sweety439 2018-10-12 17:59

[QUOTE=sweety439;497952]Why stop at 11? I suggest stop at 24

Now, I am running 12 and 13

(also, I have run 2^n-1 and 2^n+1 for n<=64)[/QUOTE]

Why you ran large prime (10^10+19)?

Now I am running 439

 MisterBitcoin 2018-10-13 18:14

Taking 3^190.

 richs 2018-10-14 00:54

6^153

Taking 6^153

 garambois 2018-10-14 14:30

OK, Updated.

1) kar_bon, n=6 updated.

2) sweety439, OK, n=12, n=13 and n=439 have been added.
I'll add n superiors when they're booked.
I ran a large prime number (10^10+19) just to see if the behavior is very different from the one with the small prime numbers.

3) MisterBitcoin : OK, done, but read point N°5) :smile:

4) richs : OK, done

5) I have tried to make the table that gives the definitions clearer on the page.
The previous explanations did not make it clear that if there is a name code, the aliquot sequence is already reserved.
I hope that with these new explanations, it's more understandable !

Thanks to all for your help !

 MisterBitcoin 2018-10-14 14:45

Sequence 3^190 lost his driver 2^2.

Meeh. Now at 306. :smile: GNFS was a bit faster. ^^

Drop 3^190

Take 12^72 12^73 12^74 12^75 12^76

Note: There was no need to add n=12; 13 and 439. These are normal sweety thinks.

Note 2: I´m not blind, but the older version was a bit .....misunderstand-able.

 MisterBitcoin 2018-10-14 14:50

12^72 terminates
12^74 terminates

Sequence 12^72 terminated at index 56 with the prime 742289.
Sequence 12^74 terminated at index 9 with an P44.

 MisterBitcoin 2018-10-14 16:59

12^76 terminates at index 67 with P11.
12^78 terminates
12^80 terminates

Take 12^77 [STRIKE]12^78[/STRIKE] 12^79 [STRIKE]12^80[/STRIKE]

 MisterBitcoin 2018-10-14 20:05

Terminations

12^82 (anonym)
12^84 (anonym)
12^86 (by me)

 RichD 2018-10-15 13:27

11^103 terminates - with a p72.

 garambois 2018-10-15 19:17

OK, that's all done.
Please report any booking errors to me.
Thank you for your help.

 RichD 2018-10-15 20:19

13^79 terminates with a p13.

 richs 2018-10-15 22:34

6^93 aliqueit: [CODE]Verifying index 98... Sequence merges with earlier sequence
1964525685310696048861640520577309969855714580014343466931029624497848886 = 2 * 61 * 6343 * 224951 * 432261855658664827 * 26107682809895863587997006586579985155412533[/CODE]

 LaurV 2018-10-16 07:52

It means nothing, you must continue it until it ends or you are getting bored of it. Aliqueit gives this message when a term lower than the starting term is reached (which makes sense when we work all sequences from 0 to 3M in order, as we usually do, we merge the higher sequence into the lower one, but in this context, unless we are going to work all sequences starting with 73 digits... :razz: we do not know what the lower sequence does, so it makes no sense to stop here).

Aliqueit has a continuation switch that allows it to continue working in this case, use it.

 kar_bon 2018-10-16 11:13

11^14 terminates in p=41

After reaching the 120-digit level at index 1000 (with a 2^4) I decided to continue and getting the downdriver at index 1008. Lucky falling for more than 110 digits after a small increase.

 richs 2018-10-16 13:17

[QUOTE=LaurV;498121]It means nothing, you must continue it until it ends or you are getting bored of it. Aliqueit gives this message when a term lower than the starting term is reached (which makes sense when we work all sequences from 0 to 3M in order, as we usually do, we merge the higher sequence into the lower one, but in this context, unless we are going to work all sequences starting with 73 digits... :razz: we do not know what the lower sequence does, so it makes no sense to stop here).

Aliqueit has a continuation switch that allows it to continue working in this case, use it.[/QUOTE]

I had not reserved 6^93; I was using it to play with aliqueit on a number with a fair number of digits. Just found it interesting.

 MisterBitcoin 2018-10-16 20:30

Drop 12^75, C108 cofactor not ECM´ed.

 garambois 2018-10-21 17:32

All is done.
Thank you for your help !

 garambois 2018-10-25 08:38

I would like to thank a lot Karsten Bonath once again.
He has further improved the page by adding tooltips that show aliquot sequence merges.

Now, the page contains even more information about "[URL="http://www.aliquotes.com/aliquotes_puissances_entieres.html"]Aliquot sequences starting on integer powers n^i[/URL]".

:smile:

 RichD 2018-10-25 11:47

12^94 terminates with a p74.

 kar_bon 2018-10-25 14:13

12^88 and 12^96 terminate

Merge for n=12^35
35 380 3876:i5

 LaurV 2018-10-26 10:40

I have just seen (and factored) the C112 which enabled the termination of 6^146. (edit: [URL="http://factordb.com/aliquot.php?type=1&aq=6&pow=146"]Stone drop[/URL]...)

 kar_bon 2018-10-28 14:18

7^139 and 7^141 terminate.

 RichD 2018-10-28 23:43

Terminates:
13^91 with a p6.
13^93 (not by me).

 garambois 2018-10-29 09:22

All is done.
Thank you !

Note : As for me, I have completed the calculations for n=2^478, terminate with a p28.

The calculations become very long for these great powers of 2 !

 kar_bon 2018-11-01 14:10

Terminates:
6^152
6^154

 richs 2018-11-03 01:36

[QUOTE=richs;498013]Taking 6^153[/QUOTE]

Dropping 6^153 (ECM'ed C121). Added 77 iterations and briefly lost the 3, but I've lost interest with the continuing 3.

 richs 2018-11-03 15:40

Terminates:

439^39 with a P73

 richs 2018-11-03 20:20

Terminates:

439^43 with a P20

 RichD 2018-11-04 02:46

13^87 terminates.

 richs 2018-11-04 13:57

Terminates:

439^45 with a P102

 MisterBitcoin 2018-11-05 14:05

Dropping all reservations, in order to clean FDB´s composite list.

Drop 12^73

Drop 12^77

Drop 12^79

No pretesting done on these numbers.

 garambois 2018-11-05 21:00

Sorry, I can't do anything right now, FactorDB doesn't work normally ! I will try again in a few days...

 garambois 2018-11-10 18:25

OK, all is done.
Thank you very much for your help !

As for me, I have completed the calculations for n=2^476, finished with a p77.
And now, all (10^10+19)^i are up to 120 digits for i from 1 to 15.

 RichD 2018-11-12 00:37

Added a few hundred terms to 7^108 with nothing interesting to report.

 gd_barnes 2018-11-17 07:26

I tested all of n=5 up to size 102 and cofactor of 96 (fully ECM'd). Here are the updates:

5^112 +137 iterations
5^114 +88
5^118 +28
5^122 +30
5^126 +18
5^128 +32
5^130 +35
5^132 +20
5^138 +34
5^140 +1449 (A wild ride!)
5^142 +32
5^164 +1 (The elves had already done this one.)

No reservations.

I am also working on all of n=6. No reservations. I'll be done in ~2 days.

 RichD 2018-11-17 17:49

Added 1000+ lines to 439^34.

 gd_barnes 2018-11-19 11:16

I tested all of n=6 up to size 102 and cofactor 97 (fully ECM'd). Here are the updates:

6^47: 1638 U104 (100) +47 iterations
6^51: 220 U108 (97) +4
6^53: 765 U103 (99) +80
6^57: 889 U102 (100) +35
6^59: 242 U107 (101) +16
6^61: 700 U102 (99) +183
6^63: 421 U111 (108) +39
6^65: 417 U103 (99) +48
6^69: 1291 U110 (103) +141
6^71: 224 U102 (100) +96
6^73: 1053 U106 (102) +777 (!)
6^75: 267 U106 (100) +56
6^83: 1029 U102 (97) +8
6^85: 544 U108 (98) +67
6^91: 167 U111 (97) +27
6^93: 1072 U102 (98) +11
6^95: 2370 U102 (99) +2319 (Dropped to 9 digits!!)
6^97: 550 U109 (103) +7
6^99: 178 U102 (100) +116
6^101: 1746 U104 (103) +19
6^103: 519 U106 (103) +104
6^105: 394 U102 (100) +9
6^107: 93 U104 (97) +28
6^109: 93 U104 (100) +46
6^111: 124 U104 (98) +53
6^113: 174 U102 (101) +142
6^115: 97 U108 (100) +56
6^117: 966 U111 (99) +7
6^119: 136 U102 (98) +100
6^121: 149 U107 (99) +119
6^127: 22 U106 (100) +6

I also extended a couple of n=5 from my previous posting from cofactor 96 to 97 (fully ECM'd):
5^118: 269 U104 (98) +42 iterations
5^156: 8 U110 (109) +1

All base 5 and 6 are now size>=102 and cofactor >=97.

I am now working on all of n=7 testing to the same limit. I'll be done in ~2-3 days.

No reservations.

 kar_bon 2018-11-19 15:43

1300 lines done on 11^46, now at 121 digits.

 garambois 2018-11-19 18:15

OK the web page is updated.

Thank you very much to all for your help !

:smile:

On my side, I finished the aliquot sequences 2^477 (one more green cell !).
And 3^136, 3^137, 3^140, 3^142, 3^157 and 3^160 are now size >= 10^120.
So, that makes 6 more orange cells in the table of base 3 !

And I think someone calculated terms from sequence 2^490.
It cannot be moved from index 3 to index 7 on its own !
The prime numbers that factor these terms are too large.
Please do not calculate the sequences already reserved.

:brian-e:

 science_man_88 2018-11-19 18:41

[QUOTE=garambois;500510]OK the web page is updated.

Thank you very much to all for your help !

:smile:

On my side, I finished the aliquot sequences 2^477 (one more green cell !).
And 3^136, 3^137, 3^140, 3^142, 3^157 and 3^160 are now size >= 10^120.
So, that makes 6 more orange cells in the table of base 3 !

And I think someone calculated terms from sequence 2^490.
It cannot be moved from index 3 to index 7 on its own !
The prime numbers that factor these terms are too large.
Please do not calculate the sequences already reserved.

:brian-e:[/QUOTE]

what other use of powers() in PARI/GP are there ?

 gd_barnes 2018-11-19 23:45

7^96 term 1267 merges with sequence 4788 term 6 with a value of 60564.

Sequence 4788 is being worked on by the main project.

7^96 is now at term 13777, size 203, cofactor size 174 !!

I'm guessing that this is now the longest n^i sequence.

:smile:

 gd_barnes 2018-11-20 07:01

[QUOTE=sweety439;497952]Why stop at 11? I suggest stop at 24

Now, I am running 12 and 13

(also, I have run 2^n-1 and 2^n+1 for n<=64)[/QUOTE]

[QUOTE=sweety439;497955]Why you ran large prime (10^10+19)?

Now I am running 439[/QUOTE]

[QUOTE=MisterBitcoin;498044]
Note: There was no need to add n=12; 13 and 439. These are normal sweety thinks.
[/QUOTE]
Sweety is not a serious searcher. He just reserves stuff, searches for a little while to a very low search-depth, and then waits for others to extend his searches. You can release all of his reservations for n=12, 13, and 439.

 richs 2018-11-20 14:53

I have been running 439^32 and 439^34 on a non-reservation basis.

 kar_bon 2018-11-20 16:13

11^30 done to 120 digits

 garambois 2018-11-20 18:04

[QUOTE=science_man_88;500514]what other use of powers() in PARI/GP are there ?[/QUOTE]

Sorry, but I don't exactly understand your question ?

 garambois 2018-11-20 18:14

[QUOTE=gd_barnes;500541]Sweety is not a serious searcher. He just reserves stuff, searches for a little while to a very low search-depth, and then waits for others to extend his searches. You can release all of his reservations for n=12, 13, and 439.[/QUOTE]

OK, I'll do that in the next week !

And thank you !
I think you're right : 7^96 is now the longest n^i sequence !
Beautiful !

richs and kar_bon thank you too.
I'll update the web page in the next week !

:smile:

 science_man_88 2018-11-20 19:33

[QUOTE=garambois;500585]Sorry, but I don't exactly understand your question ?[/QUOTE]

yeah I was semi joking just thinking of PARI /GP that could be useful.

 gd_barnes 2018-11-21 08:38

13^30 term 728 merges with sequence 3876 term 11 with a value of 39664.

Sequence 3876 is being worked on by the main project. The reservation for 13^30 can be removed.

 garambois 2018-11-21 08:41

[QUOTE=science_man_88;500596]yeah I was semi joking just thinking of PARI /GP that could be useful.[/QUOTE]

OK, I see.
The problem is that I have a very poor command of English.
So I often use machine translation.
You must have noticed it !
So I don't always understand some of the subtleties of some messages !

gd_barnes, thank you !

 LaurV 2018-11-21 09:56

Hey Jean-Luc, Maybe you can add base 28 too... I added few factorization to the DB for 28^n.
I saw you added higher bases, like 439 (?) and I don't know what reason you had, but my opinion is that 28 makes more sense than 439 or 10^x (6^n, 28^n or even 496^n can be seen as powers of perfect numbers, or "powers of drivers", in fact that was what "tickled" my interest for base 6 in the past).

 garambois 2018-11-21 20:52

OK, the web page is updated.
Thanks to gd_barnes, richs, kar_bon and LaurV for your calculations and proposals !

[QUOTE=LaurV;500655]Hey Jean-Luc, Maybe you can add base 28 too... I added few factorization to the DB for 28^n.
I saw you added higher bases, like 439 (?) and I don't know what reason you had, but my opinion is that 28 makes more sense than 439 or 10^x (6^n, 28^n or even 496^n can be seen as powers of perfect numbers, or "powers of drivers", in fact that was what "tickled" my interest for base 6 in the past).[/QUOTE]

LaurV, I added base 28.
I think that's a good idea !
Besides, it's quite odd that there are only green and blue cells for the moment, but it must be a coincidence !

[U]Some explanations[/U]

This web page (aliquot sequences that start on n^i) exists because we have an annoying question on this other web page : [URL]http://www.aliquotes.com/existence_suite_nombre_fini_primes.htm[/URL] (but sorry in french !).
To try to summarize the question in English :
[I][B]Can there be an indefinitely growing aliquot sequence in which all terms would be composed of a finite number of prime numbers, but could have any powers ?[/B][/I]
We think the answer to that question is "no", but we don't know how to tackle this problem ! However, we would like to get rid of this issue, because we have programs that may be running unnecessarily and are trying to find such aliquot sequences.
The basic idea is therefore to calculate the aliquot sequences that start on integer powers of prime numbers in a first step.
We try very small primes (2, 3, 5...), larger one (439) and a very large one (10^10+19).
We are trying to see if we could "notice" something in the behaviour of these aliquot sequences.
We also do some calculations with slightly composed numbers:
6, 10, 12, 28...
But later, if many people help us with the calculations, we would also like to add the bases with as many prime numbers as possible:
2*3, 2*3*5, 2*3*5*7, 2*3*5*7*11, 2*3*5*7*11*13, .............., and more generally p# with p=53 at least !
Thus, we will observe if the aliquot sequences behave very differently and especially which prime numbers appear in the decomposition of the successive terms of these aliquot sequences.

I hope my explanations are clear !

 LaurV 2018-11-22 02:18

How often are they updated from the DB?

(for the new addition of 28, the table needs to "pick up" another ~22 green cells, as almost all even powers in the table terminate, some were already terminated by the DB elves, some just needed a little push).

One observation: is it possible to transform javascript links in hard links? One reason, beside of the fact that few people here are scared of javascript (Hello Retina! :razz:), is that the js links are hiding the real link until it is clicked, and when clicked, it opens in another window. If I want to open 5 of them in the same time for comparisons or whatever stupid reason I may have, then I end up with 6 different browsers (including the initial one) floating around my monitors. There is also no way to right click it and tell what to do with the link (like copy it or open it in another place/tab/etc). This looks like a hacker site that deliberately hides the links, and functionally, it is a bit bothering when we want to open more (or all) sequences at once and have them in different tabs in the same browser (actually, impossible to do without heavily altering firefox behavior, because the js link is bypassing the ff's "Open links in tabs instead of new windows" settings).

The "best" workaround I found up to now is to just click the link, then combine the two browsers in one by dragging the tab from the new one to the old one where I have the other tabs. This is easy, but it has the inconvenient that it switches the view to the new tab (well, guess what! I want too much, haha).

About the colors, yes, the "missing" one is orange, but functionally, there is no difference on your site between "orange" and "no color". They all are open sequences, or unknown, or however you want to call them. But I assume your affirmation was a joke related to the fact that you expect(ed) few of us (me) to reserve few of those sequences and work them higher than 120 digits. But don't worry, that time will come...

 science_man_88 2018-11-22 02:54

[QUOTE=LaurV;500699]

One observation: is it possible to transform javascript links in hard links? One reason, beside of the fact that few people here are scared of javascript (Hello Retina! :razz:), is that the js links are hiding the real link until it is clicked, and when clicked, it opens in another window. If I want to open 5 of them in the same time for comparisons or whatever stupid reason I may have, then I end up with 6 different browsers (including the initial one) floating around my monitors. There is also no way to right click it and tell what to do with the link (like copy it or open it in another place/tab/etc). This looks like a hacker site that deliberately hides the links, and functionally, it is a bit bothering when we want to open more (or all) sequences at once and have them in different tabs in the same browser (actually, impossible to do without heavily altering firefox behavior, because the js link is bypassing the ff's "Open links in tabs instead of new windows" settings).
[/QUOTE]
No dev tools? copy the link from there ?

 LaurV 2018-11-22 03:54

[QUOTE=science_man_88;500701]No dev tools? copy the link from there ?[/QUOTE]
Grrrr... :rant:

 kar_bon 2018-11-22 16:13

28^17 terminates

 garambois 2018-11-22 21:04

[QUOTE=LaurV;500699]How often are they updated from the DB?
(for the new addition of 28, the table needs to "pick up" another ~22 green cells, as almost all even powers in the table terminate, some were already terminated by the DB elves, some just needed a little push).
[/QUOTE]

OK, updated.
For the moment, I have put an "A" for the new aliquot sequences completed for base 28.
Tell me in front of which finished aliquot sequences I should write your name.

[QUOTE=LaurV;500699]
One observation: is it possible to transform javascript links in hard links? One reason, beside of the fact that few people here are scared of javascript (Hello Retina! :razz:), is that the js links are hiding the real link until it is clicked, and when clicked, it opens in another window. If I want to open 5 of them in the same time for comparisons or whatever stupid reason I may have, then I end up with 6 different browsers (including the initial one) floating around my monitors. There is also no way to right click it and tell what to do with the link (like copy it or open it in another place/tab/etc). This looks like a hacker site that deliberately hides the links, and functionally, it is a bit bothering when we want to open more (or all) sequences at once and have them in different tabs in the same browser (actually, impossible to do without heavily altering firefox behavior, because the js link is bypassing the ff's "Open links in tabs instead of new windows" settings).

The "best" workaround I found up to now is to just click the link, then combine the two browsers in one by dragging the tab from the new one to the old one where I have the other tabs. This is easy, but it has the inconvenient that it switches the view to the new tab (well, guess what! I want too much, haha).
[/QUOTE]

I'll see about that next weekend.
But I don't know the code to make these changes.
It was Karsten Bonath who kindly proposed to create this page, I would have been unable to do so !
I'm not even really sure I understand your request.... for the moment !

[QUOTE=LaurV;500699]
About the colors, yes, the "missing" one is orange, but functionally, there is no difference on your site between "orange" and "no color". They all are open sequences, or unknown, or however you want to call them. But I assume your affirmation was a joke related to the fact that you expect(ed) few of us (me) to reserve few of those sequences and work them higher than 120 digits. But don't worry, that time will come...[/QUOTE]

I am really very happy with all the help you are all providing !
And I know what a constraint it is to push the calculations for a series of aliquot sequences to 120 digits.
Everyone does everything they can and any contribution is welcome, however modest.
There is no difference between white cells and oranges, that is true.
I think that when a cell is orange, the calculations are already quite advanced and that should be enough.
Anyway, it would take far too long in computing time to push beyond 10^120 !
And it would already do a great service if someone added even a few iterations, even 60 or 80 digits to a single aliquot sequence !

 kar_bon 2018-11-23 07:37

11^60 reaches 120 digits

 kar_bon 2018-11-23 08:54

After adding ~3700 lines to 28^21 it merges at index 4035 with 818880:i7

 kar_bon 2018-11-23 10:16

11^32 reached 123 digits

 gd_barnes 2018-11-23 10:35

I tested all of n=7 up to size 102 and cofactor 97 (fully ECM'd). Here are the updates:

7^44: 762 U104 (101) +11 iterations
7^50: 498 U106 (103) +70
7^52: 787 U103 (101) +48
7^54: 444 U104 (98) +26
7^56: 2647 U105 (97) +80
7^60: 401 U103 (102) +54
7^62: 2124 U106 (97) +1001
7^64: 1564 U102 (98) +1386
7^66: 382 U103 (97) +25
7^68: 2669 U107 (97) +115
7^70: 1574 U105 (101) +6
7^72: 170 U104 (98) +80
7^74: 135 U102 (97) +21
7^76: 325 U102 (98) +25
7^78: 157 U103 (100) +65
7^80: 1709 U105 (103) +79
7^82: 401 U102 (98) +35
7^84: 2562 U105 (100) +24
7^86: 239 U105 (97) +4
7^90: 839 U102 (97) +785
7^92: 1468 U103 (102) +1411
7^94: 632 U102 (97) +78
7^96: 13777 U203 (174) +1221 (As previously reported, merged with 4788 at term=1267!)
7^98: 1357 U102 (99) +54
7^100: 1195 U105 (100) +4
7^102: 131 U102 (100) +92
7^104: 2348 U107 (99) +43
7^106: 427 U103 (97) +381
7^110: 544 U104 (97) +471
7^112: 102 U107 (102) +62
7^114: 51 U108 (102) +10
7^116: 838 U103 (98) +803
7^118: 951 U103 (97) +925
7^120: 44 U114 (102) +20

Many of these were already updated before I reported them.

I am now working on all of n=10 testing to the same limit. I'll be done in ~2-3 days.

No reservations.

 richs 2018-11-24 00:23

Reserving 439^34

 garambois 2018-11-25 16:18

[QUOTE=LaurV;500699]How often are they updated from the DB?

(for the new addition of 28, the table needs to "pick up" another ~22 green cells, as almost all even powers in the table terminate, some were already terminated by the DB elves, some just needed a little push).

One observation: is it possible to transform javascript links in hard links? One reason, beside of the fact that few people here are scared of javascript (Hello Retina! :razz:), is that the js links are hiding the real link until it is clicked, and when clicked, it opens in another window. If I want to open 5 of them in the same time for comparisons or whatever stupid reason I may have, then I end up with 6 different browsers (including the initial one) floating around my monitors. There is also no way to right click it and tell what to do with the link (like copy it or open it in another place/tab/etc). This looks like a hacker site that deliberately hides the links, and functionally, it is a bit bothering when we want to open more (or all) sequences at once and have them in different tabs in the same browser (actually, impossible to do without heavily altering firefox behavior, because the js link is bypassing the ff's "Open links in tabs instead of new windows" settings).

The "best" workaround I found up to now is to just click the link, then combine the two browsers in one by dragging the tab from the new one to the old one where I have the other tabs. This is easy, but it has the inconvenient that it switches the view to the new tab (well, guess what! I want too much, haha).

[/QUOTE]

OK, all is done !
Now, you can see the URL.

Many thanks to Karsten Bonath.
I wouldn't have been able to make the change myself !

LaurV, as I don't know exactly for which aliquot sequences you finished the calculations, I put your name for all those whose source I don't know, even if some of them were finished by the DB elves...

:smile:

The page is updated once or twice a week.
It depends on the number of people who send results.

Thank you very much too to richs, gd_barnes, Karsten Bonath for the latest calculations.

 kar_bon 2018-11-25 17:08

Note to the new links on that page, there's is a standard behavior:

- only left clicking the link will open factordb in the same window
- CTRL+left clicking will open in a new tab
- SHIFT+left clicking will open in a new window in foreground
- CTRL+SHIFT+left clicking will open in a new window in background

 gd_barnes 2018-11-26 07:10

I tested all of n=10 up to size 102 and cofactor 97 (fully ECM'd). Here are the updates:

10^49: 946 U109 (97) +3 iterations
10^53: 1114 U103 (103) +8
10^55: 960 U103 (98) +27
10^57: 739 U102 (100) +17
10^59: 1385 U104 (97) +2
10^65: 1794 U108 (103) +17
10^69: 477 U103 (101) +17
10^73: 2680 U115 (114) +23
10^75: 559 U102 (98) +445
10^83: 922 U105 (102) +63
10^85: 1526 U104 (99) +110
10^87: 301 U105 (101) +49
10^91: 1312 U102 (97) +231
10^93: 917 U102 (97) +190
10^95: 297 U102 (99) +253
10^97: 2744 U102 (99) +2657 (Dropped to 12 digits!)
10^99: 50 U105 (97) +9
10^101: 405 U104 (103) +124
10^103: 71 U113 (108) +12
10^105: 642 U111 (99) +578
10^107: 11 U107 (103) +2

Here is one tested by others or the elves:
10^51: 2128 U105 (104) +3

Many of these were already updated before I reported them.

I am now working on all of n=11 testing to the same limit. I'll be done in ~2-3 days.

No reservations.

 gd_barnes 2018-11-26 07:18

[QUOTE=kar_bon;500939]Note to the new links on that page, there's is a standard behavior:

- only left clicking the link will open factordb in the same window
- CTRL+left clicking will open in a new tab
- SHIFT+left clicking will open in a new window in foreground
- CTRL+SHIFT+left clicking will open in a new window in background[/QUOTE]

These two are incorrect:

- CTRL+left
- CTRL+SHIFT+left

It should be:
- CTRL+left clicking will open in a new tab in background
- CTRL+SHIFT+left clicking will open in a new tab in foreground

 kar_bon 2018-11-26 07:50

Seems there're different handling of those shortcuts in browesers, see [url='http://dmcritchie.mvps.org/firefox/keyboard.htm']here[/url] (see yellow rows in the middle of the page) and depends on own browser settings, too.

 gd_barnes 2018-11-28 19:15

I tested all of n=11 up to size 102 and cofactor 97 (fully ECM'd). Here are the updates:

11^44: 490 U104 (99) +8 iterations
11^48: 609 U103 (100) +6
11^50: 1406 U105 (101) +57
11^52: 446 U104 (102) +117
11^54: 237 U102 (98) +3
11^62: 400 U102 (97) +21
11^64: 514 U103 (101) +9
11^66: 477 U102 (100) +265
11^68: 761 U108 (98) +9
11^72: 848 U102 (97) +54
11^74: 1165 U108 (98) +20
11^76: 125 U103 (102) +54
11^78: 262 U107 (103) +98
11^82: 164 U108 (97) +62
11^84: 219 U109 (104) +172
11^86: 146 U102 (97) +98
11^88: 96 U105 (101) +50
11^90: 102 U103 (101) +49
11^92: 2684 U104 (102) +2560 (Dropped to 15 digits!)
11^96: 46 U104 (102) +29
11^100: 38 U116 (107) +6
11^102: 9 U108 (97) +6 11^106: 18 U113 (104) +16 11^108: 6 U114 (100) +2

I am now working on all of n=12 testing to the same limit. I'll be done in ~2-3 days.

No reservations.

 gd_barnes 2018-11-28 21:26

12^98, 12^104, and 12^106 all terminate after short runs. :smile:

 gd_barnes 2018-11-29 04:48

I added a few terms to some larger sequences:

6^139: 6 U110 (106) +4 iterations
6^141: 15 U113 (101) +13
6^143: 10 U115 (99) +7
6^145: 13 U115 (97) +9
6^147: 6 U116 (100) +2
6^149: 4 U117 (103) +1
7^130: 7 U110 (109) +3
7^136: 5 U115 (109) +2
7^138: 5 U117 (99) +3
10^116: 7 U115 (101) +2
10^118: 12 U115 (107) +8

 garambois 2018-11-29 17:44

OK all is updated.
Thanks a lot to gd_Barnes (GDB) !

 LaurV 2018-11-30 06:04

[QUOTE=garambois;500938]OK, all is done !
Now, you can see the URL.
[/QUOTE]
[QUOTE=kar_bon;500939]Note to the new links on that page, there's is a standard behavior:
[/QUOTE]
Thanks a billion. That is exactly what we expected. We use ctrl+click a lot. Our mouse has a "ctrl" button too (side button, whose function can be set, to press with the thumb). Now, if we don't ask for too much, can the links point to the "last 20" instead of "last" only? As we are already spoiled by the aliquots blue page, to see the last 20, we will avoid additional 2 clicks on the destination page. It is more encouraging when we can see the "evolution" of the driver for the last terms in the sequence. It may be only me... but it is a psychological thing..

An that being said, I will reserve the base 28 (all shown in table).

 gd_barnes 2018-11-30 06:16

I second the motion to see the "last 20" instead of the last one.

 kar_bon 2018-11-30 13:05

11^34 done to 124 digits, still got the 2^4*31 driver (C115 full ecm-ed)

 Happy5214 2018-11-30 14:58

I'll reserve 21, but I won't start work on it until my current batch of sequences is done.

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