Aliquot sequences that start on the integer powers n^i

[EdH]

For those interested, here are a couple generations of numbers that can result in 43:

Prime 43 first generation:
50 -> 43
185 -> 43
341 -> 43
377 -> 43
437 -> 43
Prime 43 second generation:
40 -> 50 -> 43
94 -> 50 -> 43
387 -> 185 -> 43
543 -> 185 -> 43
895 -> 185 -> 43
1011 -> 341 -> 43
1119 -> 377 -> 43
1299 -> 437 -> 43
1903 -> 185 -> 43
2155 -> 437 -> 43
2839 -> 185 -> 43
6103 -> 377 -> 43
6439 -> 185 -> 43
6943 -> 185 -> 43
7123 -> 437 -> 43
7291 -> 341 -> 43
8023 -> 185 -> 43
8119 -> 377 -> 43
8383 -> 185 -> 43
9019 -> 341 -> 43
10063 -> 377 -> 43
13771 -> 341 -> 43
16579 -> 341 -> 43
18283 -> 437 -> 43
18703 -> 377 -> 43
19099 -> 341 -> 43
20299 -> 437 -> 43
21331 -> 341 -> 43
22339 -> 341 -> 43
24139 -> 341 -> 43
24319 -> 377 -> 43
24931 -> 341 -> 43
25651 -> 341 -> 43
28459 -> 341 -> 43
28783 -> 377 -> 43
28891 -> 341 -> 43
29299 -> 437 -> 43
29719 -> 377 -> 43
30883 -> 437 -> 43
32743 -> 377 -> 43
33823 -> 377 -> 43
35263 -> 377 -> 43
44923 -> 437 -> 43
45499 -> 437 -> 43
46003 -> 437 -> 43
47083 -> 437 -> 43

As compared with 47:

Prime 47 first generation:
 129 -> 47
 205 -> 47
 493 -> 47
Prime 47 second generation:
 261 -> 129 -> 47
 725 -> 205 -> 47
 995 -> 205 -> 47
 1379 -> 205 -> 47
 2071 -> 129 -> 47
 2123 -> 205 -> 47
 2435 -> 493 -> 47
 2483 -> 205 -> 47
 3007 -> 129 -> 47
 4087 -> 129 -> 47
 4163 -> 205 -> 47
 5363 -> 205 -> 47
 6179 -> 205 -> 47
 6227 -> 493 -> 47
 6683 -> 205 -> 47
 7379 -> 205 -> 47
 8003 -> 205 -> 47
 9179 -> 205 -> 47
 9563 -> 205 -> 47
 10379 -> 205 -> 47
 10403 -> 205 -> 47
 13427 -> 493 -> 47
 14291 -> 493 -> 47
 19307 -> 493 -> 47
 23267 -> 493 -> 47
 25547 -> 493 -> 47
 26291 -> 493 -> 47
 29891 -> 493 -> 47
 30587 -> 493 -> 47
 33947 -> 493 -> 47
 40067 -> 493 -> 47
 41747 -> 493 -> 47
 42827 -> 493 -> 47
 49067 -> 493 -> 47

[garambois]

Originally Posted by gd_barnes

Jean-Luc,

I've noticed in the past that Yoyo usually only works on sequences up to 140 digits. Has this changed? I ask because reservations are shown for exponents of all sizes on bases 70, 71, and 73. I see that they've already advanced many of the exponents on those bases at <= 140 digits but none > 140 digits.

If this is true, then exponents > 75 could be released for all 3 bases.

Edit: Yoyo terminated 69^70 !

Gary

I remind you that on this page you can see on which sequences yoyo (i.e. yafu) actively works.
All the sequences that are not in this list are available for you to work on yourself.
But the sequences in this list are not available.
You have to give yafu time to "clean up" !
And after this cleaning, I will update the reservations, around the beginning of November, this delay seems to me reasonable.

Congratulations to yoyo for the completed calculation of the 69^70 non-matching parity sequence !

[garambois]

For the prime number 43, I can add some statistics that I had done a few years ago, thanks to my fundamental database on aliquot sequences.
But at that time, I only had the sequences up to 10,000,000 (today, 30,000,000, maybe I should make new statistics ?).
Beware, for these statistics, all sequences <10,000,000 that have a term that exceeds 10^50 are considered Open-End and so, here, we must underestimate the number of sequences that end with 43.
Here is what the statistics say.
Of the first 10,000,000 sequences that start with the integers from 1 to 10,000,000, there are :
- 666638 that end with the prime number 43.
- 456843 that end with the prime number 59.
- 437318 that end with the prime number 41.

[gd_barnes]

Originally Posted by garambois

I remind you that on this page you can see on which sequences yoyo (i.e. yafu) actively works.
All the sequences that are not in this list are available for you to work on yourself.
But the sequences in this list are not available.
You have to give yafu time to "clean up" !
And after this cleaning, I will update the reservations, around the beginning of November, this delay seems to me reasonable.

Congratulations to yoyo for the completed calculation of the 69^70 non-matching parity sequence !

Thank you for the info. I was unaware of it.

I do not know what you mean by "you have to give yafu time to clean up". Does that mean that the list on that page is out of date? In other words, why do you have to wait until November to make your page reservations match theirs? It's a little confusing for people who are unaware of the page.

[garambois]

I don't have to wait until November, I choose to do that, because I think it's a good deadline.
I don't know how long it really takes yafu to "decide" to drop a sequence and automatically remove it from this list ?
Because I understood that yafu works like that.
But at the moment, it seems to me that there are still way too many sequences in the list that yafu is likely to work on.

[gd_barnes]

Originally Posted by garambois

I don't have to wait until November, I choose to do that, because I think it's a good deadline.
I don't know how long it really takes yafu to "decide" to drop a sequence and automatically remove it from this list ?
Because I understood that yafu works like that.
But at the moment, it seems to me that there are still way too many sequences in the list that yafu is likely to work on.

Once again, thank you for the info. Now that makes sense. They are slow to remove them from the list. I will go off of their list for reservations. If I'm interested in one of their reserved sequences and it looks like they've stopped working on it, I'll ask them directly.

It's been deserted around here since the FactorDB went down. I was lucky that I had downloaded a lot of elfs for my various efforts before that happened so my machines have kept mostly busy with it all. But I'm almost done with them. I'm getting a little worried about the site. It's been ~2 days now.

I have a lot of information to enter into the DB regarding my larger exponent opposite-parity effort here. I'm done searching bases 100-195. I only have elfs saved off down to base 97 so am working on those now.

[EdH]

I've got a full set of .elfs from a recent update for all the tables. If you have some specific ones you're interested in, I can dig through and upload them.

BTW, here's the full index 2 for 7420738134810^14:

2 .      c182 = 16016867029051535909281714695624144790320582160894836559533941276246821065324848812304319999471215177629407690206509347992575037845626243418170713804242383756754000753999672887885675 = 3^5 * 5^2 * 7^2 * 11 * 13^2 * 19 * 31 * 4397223379 * 63695801008003101125656552019171763059887853 * 175449118859425685093746579891161527440802504681023093824441968053920577368008221980886615248441968625302598292789153

[gd_barnes]

Originally Posted by EdH

I've got a full set of .elfs from a recent update for all the tables. If you have some specific ones you're interested in, I can dig through and upload them.

BTW, here's the full index 2 for 7420738134810^14:

2 .      c182 = 16016867029051535909281714695624144790320582160894836559533941276246821065324848812304319999471215177629407690206509347992575037845626243418170713804242383756754000753999672887885675 = 3^5 * 5^2 * 7^2 * 11 * 13^2 * 19 * 31 * 4397223379 * 63695801008003101125656552019171763059887853 * 175449118859425685093746579891161527440802504681023093824441968053920577368008221980886615248441968625302598292789153

I was lucky. I had downloaded all of the applicable elfs for my same-parity ECM effort for sequences with starting size > 185 digits. I did that only a few hours before it went down. I started that late Thursday and it should keep me busy through early Sunday or so. I should have at least 3 terminations! :-) If the DB is not up by then, I'll ask for some from you. Between that and the opposite-parity effort here, I will be spending many hours entering stuff into the DB when it comes back up.

A lot of things here and elsewhere depend on the FactorDB. I hope that everything will be OK with it and that little to no data was lost.

[garambois]

I also have now already 2 programs down !
I hope FactorDB will come back today...

[EdH]

Good to see it's back up. I think it seems slow, as often occurs after coming back from the depths. I think it's still rebuilding some things. The sequences are taking a while to display.

Interestingly, 7420738134810^14 is still showing abundance at term 4. Most matched parity sequences turn deficient at term 1, don't they?

Are there any stats I can dig for from my end to supplement your work, Jean-Luc?

[RichD]

Reserving all prime bases below 350 for initialization. (311, 313, 317, 331, 337, 347, 349)

Base 317 can be added at the next update. I occasionally look ahead and perform some work on sequences but this one seemed to have more work than I would do part-time.