All right, thank you very much.

@Jean-Luc: I'm having difficulty with factordb for the higher orders of 2^[I]i[/I]. It won't download the elfs, which is how my scripts currently retrieve the composites to run. I think I've reached the digit level that I'll have to consider my upper bounds for now, anyway. I have done a few of the requested sequences, but not very far. Sorry about that!

What I have done includes [I]i[/I]=560, 576, 600, 612, 630 and 648.

You may have exceeded one of the hourly limits for your userid and/or IP address.

[QUOTE=EdH;553560]
What I have done includes [I]i[/I]=560, 576, 600, 612, 630 and 648.[/QUOTE]


Thanks a lot, Ed.
It's huge already !
I couldn't have done this job !
All your calculations corroborate my conjectures, except for the calculation of the sequence that starts with 2^630 : it invalidates one of my conjectures !!!


:smile: I'll present my observations very soon...

[QUOTE=RichD;553561]You may have exceeded one of the hourly limits for your userid and/or IP address.[/QUOTE]
Nope. It's something to do with the operation of the db. Take a look at 2^600:

[URL]http://www.factordb.com/sequences.php?se=1&aq=2%5E600&action=last20&fr=0&to=100[/URL]

Then look at 2^684:

[URL]http://www.factordb.com/sequences.php?se=1&aq=2%5E684&action=last20&fr=0&to=100[/URL]

2^600 has the two graph links and the "Download .elf file" link which downloads the .elf file, appropriately. They are centered on the line.

2^684 is missing the two graph links and the "Download .elf file" link is over on the left. Clicking acts like it's downloading, but no file shows up.

wget acts the same: 2^600 d/ls fine, 2^684 is empty.

I'd be interested in how it performs for you.

[QUOTE=garambois;553563]Thanks a lot, Ed.
It's huge already !
I couldn't have done this job !
All your calculations corroborate my conjectures, except for the calculation of the sequence that starts with 2^630 : it invalidates one of my conjectures !!!


:smile: I'll present my observations very soon...[/QUOTE]
Bummer on 2^630! Blame it on me.:smile:

Looking forward to the report(s). . .

[QUOTE=EdH;553568]I'd be interested in how it performs for you.[/QUOTE]

Same spastic behavior. Once the beginning term is 200 digits or more that's when things go awry.

2^660 is fine but 2^662 (200 digits) produces the same results as your 2^684.

[QUOTE=RichD;553572]Same spastic behavior. Once the beginning term is 200 digits or more that's when things go awry.

2^660 is fine but 2^662 (200 digits) produces the same results as your 2^684.[/QUOTE]
Thanks RichD. If I do any more, I'll just have to manually work them. But, as I mentioned, I'm probably nearing my boundary. If ECM doesn't factor them at least into the 16x area, I'm not inclined to run GNFS at that level right now.

[QUOTE=EdH;550299]Additionally, that [I]a[SUP]i[/SUP]+1 [/I]is a factor of[I][I] s(a[SUP](i*n)[/SUP]) [/I][/I]([I][I]n,[/I][/I] a positive even integer)[/QUOTE]

Please, Ed, is your proposal complete ?

Because if we take, for example, a=10, n=4 and i=3, we have :

s(10^(4*3)) = s(10^12) = 1499694822171
and
10^3+1 = 1001

And 1001 do not divide 1499694822171.

I run some of the 3^i for i<=96. You should update them from time2time. No need to reserve them for me.

[QUOTE=garambois;553629]Please, Ed, is your proposal complete ?

Because if we take, for example, a=10, n=4 and i=3, we have :

s(10^(4*3)) = s(10^12) = 1499694822171
and
10^3+1 = 1001

And 1001 do not divide 1499694822171.[/QUOTE]
I was just tossing out a couple things that seemed of interest. I can't do more for a few days. If it's not valid, that's fine. I'll look at it more in a few days.