Aliquot sequences that start on the integer powers n^i

[garambois]

Okay, thank you very much, Edwin !


Next update : Sunday, June 14th after 12:00 GMT.

[garambois]

Page updated.
Thanks a lot to all !
Very big breakthroughs this week...



Thank you for checking each of you for the sequences reserved for you.
I hope I haven't made any mistake and that I haven't forgotten anything !

I have not yet added base 24 of Happy5214 and my two bases of my own : 510510 and 9699690.
This will be done in the next update, when the conditions are reached.

[EdH]

How interesting! I stopped 17^10 when it reached 120 digits at index 545. Now I see it is only 100 digits and has gone through a rather large valley of over 450 more indices. Perhaps it is being run by someone else. I will leave it at index 1001 for now and see if it increases by someone else's work.

Thanks Jean-Luc, for all your work keeping the tables in order.

[Happy5214]

210^13 merges with 50064. I can't check the indices right now because FactorDB is down, but I matched my log output for that sequence with 50064 using Jean-Luc's "last 80-digit term" list.

Edit: I ran 50064 locally, and it appears 210^13:i320 = 50064:i101 is the merge point.

[EdH]

Originally Posted by garambois

. . .
If someone wants to push the calculations further for base 2, for i beyond 500, I can also extend. I don't have a computer powerful enough at the moment to extend the calculations for base 2. Base 2 is important, it is the only one for which we can know the prime numbers at the end for each sequence.

I think I will play a little here as my machines wind down from the other tables. I will try to finish the 2^500-519 row, unless I read that someone would like me to leave it for them. . .

[Happy5214]

On a whim, I tried to pass the page through the W3C validator, and it completely barfed on it. It found over 2k errors, the vast majority of which were because the ampersands in the URLs were not escaped. Just replacing "&" with "&amp;" would do wonders for the validator. There were a few other minor issues (the <meta> tag shouldn't have a slash, the <style> tag is missing the type, and there were extraneous semicolons on the headers).

On the subject of the headers (and the colored base summaries, for that matter), it's really poor form to use <a> for non-links. The headers can be changed to <h2> for semantic correctness (you can use CSS to achieve the same inline display, like it is currently, rather than the standard block display), and the summaries should be changed to <span> tags.

I don't know if this should be directed at Karsten (who I've noticed uses <a> tags for non-links elsewhere) or Jean-Luc, but these issues shouldn't be too hard to fix, especially if a script is generating the page.

On an operational note, I've finished the trivial sequences for n=24 up to 120 digits, and I've gotten the nontrivial sequences up to i=41 to 100 digits. I'll probably finish the remaining sub-100 digit sequences by the weekend. There have been a surprising number of terminations and merges thus far. I'm also releasing 3^24, 3^26, and 3^30.

[garambois]

Originally Posted by Happy5214

On a whim, I tried to pass the page through the W3C validator, and it completely barfed on it. It found over 2k errors, the vast majority of which were because the ampersands in the URLs were not escaped. Just replacing "&" with "&amp;" would do wonders for the validator. There were a few other minor issues (the <meta> tag shouldn't have a slash, the <style> tag is missing the type, and there were extraneous semicolons on the headers).

On the subject of the headers (and the colored base summaries, for that matter), it's really poor form to use <a> for non-links. The headers can be changed to <h2> for semantic correctness (you can use CSS to achieve the same inline display, like it is currently, rather than the standard block display), and the summaries should be changed to <span> tags.

I don't know if this should be directed at Karsten (who I've noticed uses <a> tags for non-links elsewhere) or Jean-Luc, but these issues shouldn't be too hard to fix, especially if a script is generating the page.

Unfortunately, I don't understand what you're saying in those three paragraphs?
But Karsten Bonath certainly understands what it's all about...

OK for the other informations.
Please, thank you for report all sequence mergers to me.
I take good note of all your messages and I will take them into account in the next update, in a few days...
Thanks a lot !

Originally Posted by EdH

I think I will play a little here as my machines wind down from the other tables. I will try to finish the 2^500-519 row, unless I read that someone would like me to leave it for them. . .

OK, I will add the exponents from 501 to 519 for base 2 in the next update.
Beware, beware, the calculations can be very long !
Normally all the sequences of base 2 will end on a prime number.
What would be very exceptional is that you discover an Open-End sequence for base 2 !
Thanks a lot !

[EdH]

Originally Posted by garambois

. . .
OK, I will add the exponents from 501 to 519 for base 2 in the next update.
Beware, beware, the calculations can be very long !
Normally all the sequences of base 2 will end on a prime number.
What would be very exceptional is that you discover an Open-End sequence for base 2 !
Thanks a lot !

No hurry on the base 2 additions. I'm experimenting with a new script that distributes CADO-NFS via Aliqueit across several machines. I expect to work each sequence to prime, in order. I have looked at the graph of many base 2 sequences and I've not seen any increase anywhere. If there are any, they might be a rare jewel, indeed, and quite worth finding.

[kar_bon]

Originally Posted by Happy5214

On a whim, I tried to pass the page through the W3C validator, and it completely barfed on it. [...]

I've sent Jean-Luc small changes of the scripts with the errors you spotted or even the W3C validator spotted.
If those changes are implemented the only warnings the validator shows are the tables with lesser columns in the last row than in the first.
Used the <a>-tags in my old pages but won't update/change there.

[garambois]

OK, page updated !
Base 24 added.
For base 2, i from 501 to 519 added.
New Karsten Bonath scripts executed.
Plus a few other requests.

I ask everyone to check that I have not forgotten one of his requests, or that I have not made a mistake.

Thank you all for your help.
And especially thanks to Karsten Bonath for the new scripts he sent me.

[EdH]

Thanks for catching that I hadn't updated 496^41. I had two machines working that one testing a couple different setups and neither one updated factordb, even though they both finished days ago. That's OK - the next update should color in the cell - the work is done.

Thanks for all the upkeep!