Aliquot sequences that start on the integer powers n^i

[gd_barnes]

Originally Posted by RichD

Base 223 can be added to the table at the next update.

Are you done working on it? If so, I'll work on some of the same-parity exponents.

[garambois]

Partially updated page.
Many thanks to all for your help.

Added base : 223.
Added exponents for the bases mentioned in the previous posts.

Please notify me of any malfunction or error.
I still haven't been able to free up enough time to update the sequences ending with a prime number in the other thread.
I've prioritized the work mentioned above to make the overall status of the project clearer.

[EdH]

@Jean-Luc: In preparation for your upcoming data harvest, would you like me to focus on something different from the other thread?

Would you rather we focus on certain bases rather than across all tables?

I'm currently in the process of updating my entire local set, which should complete tomorrow, including all the additions. After that I'll revisit my prime searches, but at this point, I can't see anything but randomness in my results. Perhaps the randomness is the pattern?

[RichD]

Originally Posted by gd_barnes

Are you done working on it?

I'm no longer working on any exponents in base 223.

[RichD]

Bases 227 & 229 can be added at the next update. All my computations are completed.

[RichD]

Initializing bases 233, 239 & 241. This should complete all prime bases up to 250.

[garambois]

Originally Posted by EdH

@Jean-Luc: In preparation for your upcoming data harvest, would you like me to focus on something different from the other thread?

Thank you very much Edwin.
I'm not sure yet when I'll start the big harvest.
It's quite possible that in July I'll be refining all my programs and testing on small samples of the data.
Some questions and comments may come during this period.
Then, after a 3-week vacation, around mid-August, I will run the big harvest and the analysis programs on the full data set.
And then we will see what happens.
Let's finish as many calculations as possible for now.

Originally Posted by EdH

Would you rather we focus on certain bases rather than across all tables?

I would intuitively say that the smaller bases should be preferred.
But it's going to be very difficult to finish all the matched parity sequences for all bases <20 by the middle of August, because there are still some nasty sequences left.

Originally Posted by EdH

I'm currently in the process of updating my entire local set, which should complete tomorrow, including all the additions. After that I'll revisit my prime searches, but at this point, I can't see anything but randomness in my results. Perhaps the randomness is the pattern?

Unfortunately, we are perhaps condemned to find only randomness !
And if we were to see something else, would we be able to realize it ?
This is the big problem.
Because apart from looking with my eyes, I don't really see how to automatically search for aligned points or worse, points belonging to a curve on sets of points as I propose in post #1360.
Algorithms that do this job must exist, but I'm afraid it's beyond my skills !

[garambois]

Originally Posted by RichD

Bases 227 & 229 can be added at the next update. All my computations are completed.

Originally Posted by RichD

Initializing bases 233, 239 & 241. This should complete all prime bases up to 250.

This is very good news, thank you very much !

[EdH]

Originally Posted by garambois

. . .
I would intuitively say that the smaller bases should be preferred.
But it's going to be very difficult to finish all the matched parity sequences for all bases <20 by the middle of August, because there are still some nasty sequences left.
. . .

But I can opt to work the 150 digits and up terms for the lower bases over working 150 and up elsewhere. I'll focus near the bottom more and see where we get. I think most of the sequences below 150 digit terms have been taken below 145. There are probably less than a dozen left in that region.

As to programming, I'll have to look back over what we may have shown interest in for the past and see what we're looking for now. I'm still looking at a more complete list of primes that cross bases, but that is proving to be quite a task and I may have to modify my approach. I did get a full update done for my local set, without any apparent db limits interfering.

[Happy5214]

Originally Posted by garambois

So we decided to work in "bearings" (I hope I have the good word here !).

I know I'm late to this discussion. I did translate "bearing" to French ("palier") and back to English and got "level", which makes much more sense to me, in case you want to use that in the future.

I'm back to working on base 210 right now, though once I'm done to 210^11, I'd like to try to initialize at least some of the remaining open sequence bases less than 1k (these all merge into Lehmer Five sequences, which are already initialized) to fill out the Open tab on the main data page.

[EdH]

Originally Posted by Happy5214

. . .
I'm back to working on base 210 right now, though once I'm done to 210^11, I'd like to try to initialize at least some of the remaining open sequence bases less than 1k (these all merge into Lehmer Five sequences, which are already initialized) to fill out the Open tab on the main data page.

Welcome back! Should I pull 210 matched parity sequences out of the other thread? The added exponents aren't showing a reserved status currently.