Aliquot sequences that start on the integer powers n^i - Page 77

EdH · 2021-02-21, 17:23

Quote:

Originally Posted by EdH

. . .
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.

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

(I did check and both of them do show index 1068. An odd coincidence?)

Quote:

Originally Posted by VBCurtis

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.

Thanks Curtis. I will work on an appropriate post, hopefully later today.

garambois · 2021-02-21, 17:42

Quote:

Originally Posted by EdH

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.)

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:

Originally Posted by EdH

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.

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

Quote:

Originally Posted by EdH

(I did check and both of them do show index 1068. An odd coincidence?)

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

garambois · 2021-02-21, 17:43

Quote:

Originally Posted by VBCurtis

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.

Thank you very much Curtis !

EdH · 2021-02-21, 18:08

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 :
Base 42 up to exponent 80.

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

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.
Are you able to give me the exponents up to which you made all the calculations for all the bases reserved for you ?
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: https://yafu.myfirewall.org/yafu/download/ali/y/

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

and, the following 35 have terminated:

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 !

@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:

Originally Posted by yoyo

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

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

2021-02-21, 18:09	#841
garambois "Garambois Jean-Luc" Oct 2011 France 2·5²·11 Posts	@yoyo : Please, I noted the following thing : Base 42 up to exponent 80. But I searched on this forum, I cannot find the following information, unless I am mistaken : Base 34 up to the exponent ??? Base 35 up to the exponent ??? Base 8589869056 until the exponent ??? 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. Last fiddled with by EdH on 2021-02-21 at 21:08 Reason: Word change per request - post #846

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2021-02-21, 18:44	#842
yoyo Oct 2006 Berlin, Germany 2²·3²·17 Posts	I start all up to exponent 100. But they fall out of my queue fast because I stop if composite is > C139.

2021-02-21, 19:10	#843
garambois "Garambois Jean-Luc" Oct 2011 France 2×5²×11 Posts	@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. Are you able to give me the exponents up to which you made all the calculations for all the bases reserved for you ? 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 !

2021-02-21, 19:19	#844
yoyo Oct 2006 Berlin, Germany 264₁₆ Posts	Here is everything I added: https://yafu.myfirewall.org/yafu/download/ali/y/

2021-02-21, 20:40	#846
garambois "Garambois Jean-Luc" Oct 2011 France 1046₈ Posts	OK perfect Edwin : everything matches ! @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 ?