Aliquot sequences that start on the integer powers n^i

[Happy5214]

n=24 is done to 100 digits. 24^17 and 24^25 both merge (24^17:i282 = 29022:i20 and 24^25:i329 = 620712:i514). I'll continue with my reserved n=3 sequences before resuming n=21.

@kar_bon: Thanks for the syntax fixes. The headers still need to be fixed, though. I wasn't expecting you to update to HTML5 (thanks for that), but since you have, the variables (n and i) should be in <var> tags instead of <i>, providing the semantics of a variable. You should also group each base under its own <section> tag. The liberal use of double <br> tags should be replaced with paragraphs using <p>.

[garambois]

OK, page updated.
Thanks to all.
Bases 510510 and 9699690 added.

[Happy5214]

I just had an idea that I think would be useful. Can we add the number of sequences that merge into "main project" sequences to the open sequence count as another parenthesized number? For example, n=3 would have "Open: 108 (108) (8) ➔ 43.03%" or something to that effect.

[garambois]

For the moment, we see no need to specify the number of Open-End sequences that merge with sequences from the "main project".
But if you say you need it, we could try to add it.
Do you confirm that you would need it ?

[Happy5214]

I'm assuming that this subproject won't continue sequences that merge into "main project" sequences, in deference to the main efforts. If so, there should be an easy way to count the number of sequences that we will continue through this subproject (in theory, at least) rather than handing off to the "main project". If added, I personally would use an at-a-glance look at merged sequences for different bases, just like I would use the terminated sequence count.

[richs]

Originally Posted by richs

I will reserve 439^14 since I'm still working it. Thanks!

439^14 is now at i2812 (added 2140 iterations) and a C130 level with a 2^3 * 3^2 * 5 driver, so I will drop this reservation. The remaining C121 term has been ecm'ed to t37.

Reserving 439^16.

[garambois]

@richs :
OK, Changes will be made at the next update. Many thanks.


@Happy5214 :
What form of display would be most convenient for your needs ? Just like this :
"Open: 108 (108) (8) ➔ 43.03%"
But in this case I'm afraid it would be difficult for a newcomer to understand what the numbers in brackets mean.
Or wouldn't it be better to put the line in this form or something to that effect :
"Open: 108 (including 108 calculated to 120 digits or more and 8 that merge with the sequences of the main project) ➔ 43.03%"
or else :
"Open: 108 (including 108 orange cells and 8 mergers) ➔ 43.03%"
If the English-speaking readers of this post have an opinion and manage to make the line as clear as possible in the shortest possible way, please choose one of these options or suggest something better.

[Happy5214]

Perhaps you could add an explanation in the Definitions section, something like this:

Below the table for a base are stats for that base's sequences. "Done" is the number of sequences terminating at primes, "Cycle" is the number of sequences terminating in a cycle, and "Open" is the number of open-ended sequences, in the format "<total open-ended sequences> (<number of sequences calculated to at least 120 digits>, <number of sequences which merge into "main project" sequences>). For example, a base with 20 total open-ended sequences, of which 10 have been calculated to 120 digits and 5 merge, would be described with "20 (10, 5)

Whether you do that or not, you should also surround the individual numbers with <abbr> tags and explain their meanings in the title= attribute.

[Happy5214]

Originally Posted by Happy5214

Whether you do that or not, you should also surround the individual numbers with <abbr> tags and explain their meanings in the title= attribute.

On second thought, it's not actually an abbreviation, so use a couple of nested <span> tags (one for each number) with the title= attribute describing what it represents. You may want to add a couple of classes and some CSS to those classes (text-decoration: underline dotted; would make it look like <abbr> in most browsers).

[EdH]

@Jean-Luc,

The 2^500-2^519 row has only three still orange, which I'm sure won't be green by your next update. But, I hope they will be green by the following update.

Since I am capable of working in that area, I could do another row (2^520-2^539), if that's where you would prefer. Or, if you have somewhere else you would prefer I work, let me know and reserve it for me.

Thanks,
Ed

Edit: Once I have turned a block orange in the tables other than base 2, I probably should be removed from that block as I no longer intend to work there, at least for now. Unfortunately, that may be a lot of work for you at this point. - sorry! If that's the case, leaving me there won't hurt me at all, but may keep others from working on those sequences.

[Happy5214]

Originally Posted by garambois

@richs :
OK, Changes will be made at the next update. Many thanks.


@Happy5214 :
What form of display would be most convenient for your needs ? Just like this :
"Open: 108 (108) (8) ➔ 43.03%"
But in this case I'm afraid it would be difficult for a newcomer to understand what the numbers in brackets mean.
Or wouldn't it be better to put the line in this form or something to that effect :
"Open: 108 (including 108 calculated to 120 digits or more and 8 that merge with the sequences of the main project) ➔ 43.03%"
or else :
"Open: 108 (including 108 orange cells and 8 mergers) ➔ 43.03%"
If the English-speaking readers of this post have an opinion and manage to make the line as clear as possible in the shortest possible way, please choose one of these options or suggest something better.

Another suggestion would be to show the merged sequence count with the same yellow background as the merged sequence links.