Aliquot sequences that start on the integer powers n^i

[RichD]

Base 43 can be added at the next update. All expected terminating sequences are terminated and all remaining composites are greater than C78.

Starting initial work on base 47.

[EdH]

Originally Posted by garambois

. . .
Did I understand correctly, you also have a C++ program that does this job faster ? This other program would also interest me.

Here is the source for a C++ program. I'm afraid it's probably a bit "amateurish," and it has very little internal commenting, but it should compile on linux with:

g++ alimerge3.cpp -o alimerge3

and can then be invoked by:

./alimerge3 37 1 80

to run the entire base 37 table. Here's an example (wrapped in date calls to provide timing)*:

$ date;./alimerge3 37 1 80;date 
Tue 16 Feb 2021 02:19:01 PM EST 
Running base 37 from 1 through 80 . . . 
37^6:i126 merges with 109920:i1275 
37^8:i151 merges with 1632:i37 
37^12:i1057 merges with 10824:i28 
37^18:i1430 merges with 3366:i2 
37^22:i519 merges with 1567300:i0 
37^30:i1193 merges with 35856:i3 
Tue 16 Feb 2021 02:22:27 PM EST

That comes in at about 3:26 to run the entire base 37 table. That's about 206 vs. 1211 seconds for the Bash version.

* I tried to add an elapsed time function, but for some reason the timing was extremely inaccurate with the several methods I tried, so I left it out.

[garambois]

Originally Posted by RichD

Base 43 can be added at the next update. All expected terminating sequences are terminated and all remaining composites are greater than C78.

Starting initial work on base 47.

OK, a lot of thanks !
The next update will be next weekend.

[garambois]

Originally Posted by EdH

Here is the source for a C++ program.

OK, a lot of thanks !
I will test this program very quickly, but I can't get it to work at the moment, I don't know why yet ?

Otherwise, more generally, in three days, I will be on vacation.
I will try to do some data analysis.
Hopefully the large amount of new data accumulated allows us to formulate new small conjectures ... that is our goal !

[EdH]

Originally Posted by garambois

OK, a lot of thanks !
I will test this program very quickly, but I can't get it to work at the moment, I don't know why yet ?

Otherwise, more generally, in three days, I will be on vacation.
I will try to do some data analysis.
Hopefully the large amount of new data accumulated allows us to formulate new small conjectures ... that is our goal !

The source code I provided works under various linux machines here, compiling with no issues. It even compiles on my RPi machines. Let me know of any errors/warnings if any occur. I do now have a version that includes timing. If I add that one, I'll still leave the other.

The source should compile on Windows, as well, but it's been so long since I've worked with Windows, that I wouldn't be able to even try.

If there is some data in particular you'd like harvested, let me know and I can try to do that as well. I'm trying to keep a local up-to-date set of all the tables, at the ready for such work.

Have a Great Vacation!

[garambois]

Most of this vacation, I am going to work on the aliquot sequences. I have already started the preliminary work, I am writing and running programs.

But I would need a little help !

Would someone be able to calculate the following sequences, but only up to index 2, and of course, to enter the results on factordb :
(9699690 * 23)^20
(9699690 * 23 * 29 * 31)^14
(9699690 * 23 * 29 * 31 * 37)^14
Indeed, my computer is very busy and that would allow me to have the results already next weekend.
I still need more sequences, but the calculations will be shorter and I can handle them.

@Edwin : I'm on a track... Since I looked again at your "2-Stats.txt" file (from here), I got a new idea because of the fourth column.

But I have to do some more analysis to be sure that it is worth it that I expose you on this forum what I noticed. The calculations I am requesting above relate to this work.

[EdH]

I have queued up index 1 for both of the first two, but they will take a little while to finish. Do you need index 2 also fully factored or just reach index 2? The bulk of my machines are running a rather large job right now, so I am somewhat limited.

[garambois]

Originally Posted by EdH

I have queued up index 1 for both of the first two, but they will take a little while to finish. Do you need index 2 also fully factored or just reach index 2? The bulk of my machines are running a rather large job right now, so I am somewhat limited.

I need just to reach index 2 but not to factor. Thank you very much Edwin !

[EdH]

Originally Posted by garambois

I need just to reach index 2 but not to factor. Thank you very much Edwin !

The first two are at index 2. The third is in work.

[garambois]

Thank you very much Ed !

[EdH]

Originally Posted by garambois

. . .
(9699690 * 23 * 29 * 31 * 37)^14
. . .

Third one is at index 2, also.

Glad to be helpful. I'm looking forward to your findings.