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-   -   Aliquot sequences that start on the integer powers n^i (https://www.mersenneforum.org/showthread.php?t=23612)

garambois 2023-03-06 20:44

OK for the typo, I will correct it for the next update.

Regarding merging with a number >3000000 outside the main project, you are right.
Normally such merges are not noted.
I don't understand how this merge can appear in the project, I don't understand its origin ?
But should I delete this information which is correct ?

EdH 2023-03-06 20:53

From post# 956:
[QUOTE=RichD;558264]I think 31^36 may have merged.[/QUOTE]I traced the merge to 3762570.

garambois 2023-03-06 22:20

It happened a long time ago.
I didn't remember it at all !
Let's put this merger on the page, since we had already discussed it in the past.

gd_barnes 2023-03-06 22:24

[QUOTE=garambois;626205]OK for the typo, I will correct it for the next update.

Regarding merging with a number >3000000 outside the main project, you are right.
Normally such merges are not noted.
I don't understand how this merge can appear in the project, I don't understand its origin ?
But should I delete this information which is correct ?[/QUOTE]

For consistency, I would delete it. But maybe store it somewhere in case the main project ever gets extended to 5M or 10M. The reason being is that there is no formal work being done on 3762570 and removing the merge info. allows our project to work on it if the interest is there. That's just my two cents.

[QUOTE=EdH;626206]From post# 956:
I traced the merge to 3762570.[/QUOTE]

I did not see anything in post 956 about it. I do see it in post 835 here:
[url]https://mersenneforum.org/showpost.php?p=572146&postcount=835[/url]

That was in response to posts 830 and 833.

It appears that Jean-Luc thought you had an error in your script causing it to not find a merge. In fact, there was no error if your script was only looking for merges with sequences <= 3000000.

gd_barnes 2023-03-07 01:00

I found a typo for the 239^6 merge:

The page states:
239^6:i1681 merges with 2667000:i1

It should be:
239^6:i681 merges with 2667000:i1

1681 vs. 681

This one stuck out at me because it is the only merge on the n^i project in Karsten's new list that is at current size < 136 digits. It's only at 120 digits.

EdH 2023-03-07 01:23

[QUOTE=gd_barnes;626213]. . .
I did not see anything in post 956 about it. I do see it in post 835 here:
[url]https://mersenneforum.org/showpost.php?p=572146&postcount=835[/url]

That was in response to posts 830 and 833. . .[/QUOTE]The number should have been [URL="https://www.mersenneforum.org/showthread.php?p=558264#post558264"]596[/URL] instead of 956. That's where RichD first brought it up.

garambois 2023-03-08 09:11

[QUOTE=gd_barnes;626220]I found a typo for the 239^6 merge:

The page states:
239^6:i1681 merges with 2667000:i1

It should be:
239^6:i681 merges with 2667000:i1
[/QUOTE]
Congratulations for noticing this new error !
I hope there are no more like it !
Of course, I will correct it in the next update.

garambois 2023-03-08 09:26

[QUOTE=gd_barnes;626213]For consistency, I would delete it. But maybe store it somewhere in case the main project ever gets extended to 5M or 10M. The reason being is that there is no formal work being done on 3762570 and removing the merge info. allows our project to work on it if the interest is there. That's just my two cents.
[/QUOTE]
Thank you Gary for your opinion, that's how we move forward.
I think the main project should be expanded to at least 4 or 5 million in not too long.
Indeed, it has been a very long time since it has been expanded.
So this sequence will inevitably move forward in a while.
And since this information about its fusion is quite valid, I think I'll leave it for now.
If this sequence should be of particular interest, we will soon notice again that it is not included in the main project if the main project should not be extended and we could then add the terms that we need.

gd_barnes 2023-03-08 09:45

[QUOTE=garambois;626304]Thank you Gary for your opinion, that's how we move forward.
I think the main project should be expanded to at least 4 or 5 million in not too long.
Indeed, it has been a very long time since it has been expanded.
So this sequence will inevitably move forward in a while.
And since this information about its fusion is quite valid, I think I'll leave it for now.
If this sequence should be of particular interest, we will soon notice again that it is not included in the main project if the main project should not be extended and we could then add the terms that we need.[/QUOTE]

OK. Sounds like a good explanation to me.

One of the sequences that I tested to 120 digits in the last few months dropped to between 3000000 and 4000000 3 or 4 different times but it somehow did not merge with the main project. I will see if I can find it. Maybe you can note it as merged also.

Maybe someone can do a merge analysis looking for merges with sequences < 5000000.

gd_barnes 2023-03-08 09:53

I found the sequence from the previous post that I was talking about. It is 401^8. See here:
[url]https://mersenneforum.org/showpost.php?p=618494&postcount=2082[/url]

It dropped as low as 3086468 at index 1061 and had 5 indexes in that area that were < 4000000. Since it never merged with any sequences < 3000000, 3086468 is likely the merge sequence. If so:

401^8:i1061 merges with 3086468:i0

This was very unusual!

Is this the type of sequence you want to show a merge for? It's even more obvious than 31^36.

gd_barnes 2023-03-08 14:00

I know, I'm kind of spamming the threads...

I have completed testing of new base 110 all open sequences to >= 120 digits.


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