Aliquot sequences that start on the integer powers n^i

[gd_barnes]

Originally Posted by EdH

I found that you had included most of the reserved bases that have not been added to the tables yet. I included all of them. That's why 1264460^18 shows up for prime 3. I've only done a little bit of spot checking, so the file would need serious validation before it is considered correct.

My program shows 7460 unique terminating primes, with a total of 9549 terminated sequences.

* whole set, in this case, means all the bases that have tables, plus all the reserved bases that are mentioned near the top of the main page. However, the sequences that the db won't provide valid .elf files for are not currently included. i will address these eventually, but not for now, since none of them are currently terminated.

Is there an explanation for why the prime 43 terminates so many more sequences than any others?

[garambois]

In the main project, the same is true.
It is by far the prime number 43 that is the end of the largest number of sequences.
This is not only true for our project n^i.
I don't know if anyone has an explanation ?

[garambois]

Originally Posted by EdH

It was long awaited, but I finally have a C++ program that scours the whole set* in 15 seconds. There is a little bit of difference as explained further below. Here is the same set (with a highlighted difference for prime 3) as shown in post #1845:
...
...
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My program shows 7460 unique terminating primes, with a total of 9549 terminated sequences.
...
...

Thank you very much Edwin.
I will study this closely soon enough.
I attach the result given by Karsten's scripts.
So we get the result in three different ways.
Karsten's script gives this in a few seconds.
A lot of thanks to Karsten !
We still have to check that our three lists match: the one in post #1845, the one in post #1877 and this post.
I don't have time to do that in theI don't have time to do that in the next 2 or 3 days.

[kar_bon]

You missed prime 257 as ending in the new "graph.txt".

There're some bases which are not listed taken in the first attempt and some newly terminated seqs, too.
Bases like 780, 828, 888 or terminations like 26^110.

In your first file there're some extra spaces. I will send you a small update of my script to change the output format to the others, so you can catch differences easier.

[EdH]

Agree that matching the formatting will be necessary to employ software verification. My program outputs a different format, as well, but I can make two search/replace edits to match Jean-Luc's format. (I also removed the extra spaces from Jean-Luc's list for the comparisons I did.)

Matching for updates will be challenging. I'm always amazed at how much has changed within a few days. Now that the newer db limits are in place, what used to take less than an hour is taking 18 hours. I could probably shorten that by watching more closely, but for now, it works comfortably without reaching the limits.

I am contemplating a program that would work directly with the db just checking last lines. It should be able to do the entire set without hitting the limits, but it would be much slower than the current 15 seconds using the local set. The advantage would be up to date results, but that may not really be a major issue ATM.

[garambois]

Thank you very much Karsten.
I hadn't seen about 257 !
Yes, I am missing a few bases, but I am almost done with 780.
It's true that for bases 396, 696, 780, 828, 888 and 996, there will be many more than in post #1845.
At first glance, our three programs are a good match.
Edwin, I also don't think it's a major problem if we don't have the data exactly up to date to the day.
The prime numbers 601 and 761 should be included in my study, it seems to me.
I also note that the Mersenne primes have at least three sequences, contrary to others "of comparable size" but this is quite normal if one thinks a little.

[warachwe]

Originally Posted by gd_barnes

Is there an explanation for why the prime 43 terminates so many more sequences than any others?

Originally Posted by garambois

In the main project, the same is true.
It is by far the prime number 43 that is the end of the largest number of sequences.
This is not only true for our project n^i.
I don't know if anyone has an explanation ?

I think, with no evidence to back it up, it might be because 43 have many values of "reverse aliquot" (don't know what it's actually called) in the first few terms. So it's more like grouping sequence that "end" in those numbers together.

Maybe we can try to compare the number of , say, 6 digits "reverse aliquot" of each prime with the number of sequences that end with that prime?

[gd_barnes]

I like the idea that 43 could come from quite a few numbers in the reverse aliquot situation. That is the iteration before the number 43 could theoretically be many different values. It would be interesting to see an analysis of that.

[gd_barnes]

Jean-Luc,

I've noticed in the past that Yoyo usually only works on sequences up to 140 digits. Has this changed? I ask because reservations are shown for exponents of all sizes on bases 70, 71, and 73. I see that they've already advanced many of the exponents on those bases at <= 140 digits but none > 140 digits.

If this is true, then exponents > 75 could be released for all 3 bases.

Edit: Yoyo terminated 69^70 !

Gary

[VBCurtis]

Originally Posted by warachwe

I think, with no evidence to back it up, it might be because 43 have many values of "reverse aliquot" (don't know what it's actually called) in the first few terms. So it's more like grouping sequence that "end" in those numbers together.

Maybe we can try to compare the number of , say, 6 digits "reverse aliquot" of each prime with the number of sequences that end with that prime?

This was exactly my conclusion too.

[EdH]

Releasing base 98.