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

EdH 2021-02-21 17:23

[QUOTE=EdH;572138]. . .
Darn! I had intended to run Aliqueit against all the sequences before compiling the list and totally forgot about it.

Thanks for looking after me, Happy5214.

As to the possible Team Project suggestion, I'll look into this at some point.[/QUOTE]I have run the entire set through Aliqueit and found two broken sequences. I have not yet explored further:
[code]
1750944 ERROR: @index 1068: value != sigma - n
2796840 ERROR: @index 1068: value != sigma - n
[/code](I did check and both of them do show index 1068. An odd coincidence?) [QUOTE=VBCurtis;572150]When you're ready to do some work on that sequence, make a thread for it in the same place as the 3366 and 4788 threads. Sean and I will surely help with ECM and other work- as you observe, most of the current team sequences are over 200 digits and rather difficult to work on.[/QUOTE]Thanks Curtis. I will work on an appropriate post, hopefully later today.

garambois 2021-02-21 17:42

[QUOTE=EdH;572138]I think this might be less extraordinary than its first impression. The other sequences merge at different values with each other and then the one with lowest connection with the smallest valued sequence merges and all take on the lowest value. I think it's just a small portion of the genealogy work we did long ago with certain sequences capturing many others along the way. (Or, maybe I'm missing something early in my morning.)
[/QUOTE]

The future will tell !
I have a hunch that this will lead us to notice some interesting things, but it's only a hunch at the moment !


[QUOTE=EdH;572146]Ah, yes! The reason it is not found is because a fresh copy of your 2020 80 digit file only goes to 3M, and 3762570 is above that cut. I have a local file which has that entry added, so it is found against that file, but not against the original. The list I provided also ends prior to 3M.[/QUOTE]

OK, I understand what's going on !
Thanks !


[QUOTE=EdH;572153](I did check and both of them do show index 1068. An odd coincidence?) [/QUOTE]

This is strange !
I will also be checking in the next few days ...

garambois 2021-02-21 17:43

[QUOTE=VBCurtis;572150]When you're ready to do some work on that sequence, make a thread for it in the same place as the 3366 and 4788 threads. Sean and I will surely help with ECM and other work- as you observe, most of the current team sequences are over 200 digits and rather difficult to work on.[/QUOTE]


Thank you very much Curtis !

EdH 2021-02-21 18:08

2 Attachment(s)
Here are the corrected .elfs for the two broken sequences. I need to do some other things before I post a new C80 list.

garambois 2021-02-21 18:09

@yoyo :

Please, I noted the following thing :
[I]Base 42 up to exponent 80.[/I]

But I searched on this forum, I cannot find the following information, unless I am mistaken :
[I]Base 34 up to the exponent ???
Base 35 up to the [/I][I][I]exponent[/I] ???
Base 8589869056 until the exponent ???[/I]

Can you please provide me with that information ?
If not, I will look at FactorDB to try and see how far the calculations have been made, but doing so can lead to errors.

Thank you very much.

yoyo 2021-02-21 18:44

I start all up to exponent 100.
But they fall out of my queue fast because I stop if composite is > C139.

garambois 2021-02-21 19:10

@yoyo :

OK.
Is base 42 up to exponent 100 too ?

I just randomly checked for base 20.
I think you also calculated the sequences up to the exponent 100 for this base !
And the project page only goes up to exponent 92 for base 20.
I'm not sure the project page shows all of the calculations that were done by yafu.
[B]Are you able to give me the exponents up to which you made all the calculations for all the bases reserved for you ?[/B]
If not, I can try to find this information in another way, but I think it would be a bit laborious !
So we would see all the work that has been done by yafu.
This job is even more important than I thought.
It is very easy for me to add exponents for bases.

Many thanks !

yoyo 2021-02-21 19:19

Here is everything I added: [url]https://yafu.myfirewall.org/yafu/download/ali/y/[/url]

EdH 2021-02-21 20:16

I've managed to resolve the missing 51 sequences from the 2020 list to the new list. One was the troublesome 1750944.*

Next, 15 have merged:
[code]
399296^1:i5182 merges with 316960:i3
1444668^1:i6883 merges with 21546:i69
1999854^1:i2024 merges with 52374:i647
2073120^1:i5555 merges with 3876:i11
2212008^1:i1989 merges with 418080:i3
2324490^1:i5000 merges with 33870:i12
2338548^1:i3683 merges with 2127104:i7
2400840^1:i3436 merges with 17544:i6
2422868^1:i4216 merges with 14320:i25
2435784^1:i2709 merges with 1135584:i538
2482794^1:i1832 merges with 584802:i105
2502990^1:i2073 merges with 487172:i10
2506536^1:i1367 merges with 239700:i23
2545956^1:i3429 merges with 49236:i6
2564484^1:i2066 merges with 79842:i17
[/code]and, the following 35 have terminated:
[code]
95448
306408
1739160
1928262
1991080
2055144
2110320
2229246
2279670
2325636
2356674
2358432
2378952
2380158
2383668
2408226
2428320
2448564
2453022
2457000
2463636
2466132
2475000
2484054
2496648
2499000
2503284
2504334
2515536
2540610
2546472
2546760
2548404
2588238
2620074
[/code]1 + 15 + 35 = 51. So, all 51 are accounted for, if all my research is correct.

* 1750944 and 2796840 are now corrected in my set, and I'm running Aliqueit against the entire set again. The next run "should" provide a new complete up-to-date list. I will remove the earlier one I posted and attach the new one to a new post when I have it complete.

Thanks for all the help, everyone.

garambois 2021-02-21 20:40

OK perfect Edwin : everything matches !

:smile:



@All : This is a detail, but of course, in post #841, replace the word "exhibitor" with "exponent".
Translation mistake !
Edwin, could you please do this unless you think it doesn't matter ?

garambois 2021-02-21 21:02

[QUOTE=yoyo;572171]Here is everything I added: [URL]https://yafu.myfirewall.org/yafu/download/ali/y/[/URL][/QUOTE]


OK, thank you very much yoyo !

So I'll add exponents on the page for most of the bases calculated by yoyo with yafu.
A lot of calculations are already done.
On the other hand, for bases greater than 200 reserved by yoyo, the exponents always go up to 100.
However, 8128^100>10^390 and 8589869056^100>10^990 !
It therefore seems unnecessary to me to increase on the page the number of exponents up to 100 for bases greater than 200.
I will proceed as below to display only reasonably computable sequences on the page :
Base 220 up to exponent 80
Base 284 up to exponent 70
Base 439 up to exponent 60
Base 496 up to exponent 60
Base 770 up to exponent 60
Base 1155 up to exponent 50
Base 8128 up to exponent 40
Base 33550336 up to exponent 25
Base 8589869056 up to exponent 20


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