Aliquot sequences that start on the integer powers n^i

[garambois]

Originally Posted by garambois

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).

Originally Posted by bur

That sounds good, I found cado to be faster than msieve. Is that script publicly avilable?

Following these two messages, I contacted Paul Zimmermann and Olivier Huber.
They both gave their agreement for me to publish here our program which calculates the aliquot sequences.
But I preferred to present this program in a new Thread, see here.
So, it will be easier to find this program in the future for those who would need it.
If, however, this program should be of interest to some of you ?

[Nescro]

I am currently working on getting all values of base 211 up to at least 100 digits in size up to i = 50.

Attached is a list of the latest i values and their statuses within the FDB.

Thank you,
Nescro

[RichD]

Base 74 can be added at the next update. There is still a bit of work to do but the cool table helps me track the progress better. No need to reserve anything in my name. Merges should be checked for these sequences too. I did a little work on base 62 also.

[garambois]

Many thanks Nescro and RichD.
I will do the next update most probably on Thursday July 8 and I will add also the bases 211 and 74.
For base 62, I will wait to hear from you.
For base 211, I can see in the attached file that we have two sequences that end on a perfect number, one of them on 8128 !
We had not yet encountered this situation in our project.

[RichD]

Originally Posted by garambois

For base 62, I will wait to hear from you.

Base 62 is already included in your tables. I simply advanced several sequences.

[EdH]

Base 450 should all be green at your next update. If no one lets me know they're already there, I'll start working on base 338, greening up the non-green cells. . .

[garambois]

Originally Posted by RichD

Base 62 is already included in your tables. I simply advanced several sequences.

Yes I know that !
But anyway, on Thursday I'm going to update all the bases of the project.
Because during the month of July, I will have a lot of periods without access to my computer.
So don't be surprised if sometimes it takes me a long time to answer on the forum, sometimes more than 15 days...

Originally Posted by EdH

Base 450 should all be green at your next update. If no one lets me know they're already there, I'll start working on base 338, greening up the non-green cells. . .

Excellent, many thanks !
The more green cells we have by August, the better.
Because I'm going to do a big data analysis.
Maybe a 141st conjecture will come out of it !
But maybe nothing will come out of it, we can't predict anything !
Nothing ever went as I had planned on this project...

[bur]

Originally Posted by garambois

Yes I know that !
But anyway, on Thursday I'm going to update all the bases of the project.

Depending on how stubborn the co-factors prove to be, I hope to have terminated all trivial sequences of 53^i for i <= 100 by then.

What would be of more interest to the project, initializing a new base or extending the non-trivial sequences of base 53 (or any other base)?

[Happy5214]

Originally Posted by garambois

Would there be a volunteer to do the preliminary work on base 19116 (C28) and base 14288 (C5) ?

Since there was no other interest in these bases, I'll take both of them and start with them later Monday or Tuesday.

Edit: I've already completed the trivial sequences for both to i=20 with a combination of FactorDB and its elves, Alpertron's ECM/SIQS calculator, and a little bit of local yafu on my laptop.

[garambois]

Originally Posted by bur

What would be of more interest to the project, initializing a new base or extending the non-trivial sequences of base 53 (or any other base)?

In the long run, Yoyo will certainly extend the non-trivial sequences of base 53.
It is therefore more interesting to initialize a new base, especially in view of the future work in August.
There are also bases which have only trivial sequences and which will be very interesting in August : the doubles of squares.
The smallest not yet initialized is 2*18^2=648.
There are also 2*19^2=722 and 2*20^2=800.

[garambois]

Originally Posted by Happy5214

Since there was no other interest in these bases, I'll take both of them and start with them later Monday or Tuesday.

Edit: I've already completed the trivial sequences for both to i=20 with a combination of FactorDB and its elves, Alpertron's ECM/SIQS calculator, and a little bit of local yafu on my laptop.

Many thanks.
I'm curious to see if anything special is going to happen,
I'm not sure what, but we better check it out !