Aliquot sequences that start on the integer powers n^i

[RichD]

Another merge 41^32 ?

Base 41 can be added at your leisure.

[Happy5214]

Originally Posted by RichD

Another merge 41^32 ?

Base 41 can be added at your leisure.

41^32:i386 = 271980:i46

Edit: I'll also take base 42 to initialize.

[RichD]

Base 41 was taken to i=77 as will base 43 be taken to the same.

[Happy5214]

Base 42 done to 80 digits (odd exponents; 42^47) and 120 digits (even exponents; 42^72), and as soon as I wrote this, I think I misread https://www.mersenneforum.org/showpo...&postcount=762 above in reference to there being a new minimum. I wasn't planning to take this base to work on past the seeding work, so I could take it to the usual 100 digits or yoyo (or someone) could take it from here.

Exponents 1, 3, and 5 terminate with primes. There were two merges: 42^11:i131=35320:i2 and 42^17:i361=239940:i3. All even exponents tested terminated with primes, including 42^34, which terminated on the first term. Interestingly, 42^16 picked up a square and became even for two terms, before picking up another square and terminating two terms later.

[garambois]

Page updated.
Thank you all for your precious help !
Thank you for reporting any errors regarding your work, your reservations, your current initializations, your mergers... The update was laborious !


Added bases : 37, 41, 392, 450, 882 and 33550336.
Bases reserved for yoyo : 439, 496, 770, 1155, 33550336.
Bases being initialized which will be added during a next update, I will wait for your signal : 34 (YOY), 35 (YOY), 42 (YOY), 43 (RFD), 578 (EDH), 8589869056 (YOY).


Edit : When I look at the tables for bases 37 and 41, I think we forgot some merges, especially for base 37 ! But sorry, I really don't have enough time today to take care of this ! I will see for the next update ...

[yoyo]

I'll take also 37, 41 and 42.

[RichD]

More merges? 43^16 & 43^34

[EdH]

Originally Posted by garambois

. . .
Edit : When I look at the tables for bases 37 and 41, I think we forgot some merges, especially for base 37 ! But sorry, I really don't have enough time today to take care of this ! I will see for the next update ...

I have a script that will run a whole table against current sequences checking for merges. I'll run it on all the new tables and see what it turns up. At that point there will be a list that can be referenced instead of digging through posts. I'll try to have that later today.

Note that it uses the 80 digit file, so it won't pick up those few merges we found that are outside that.

[garambois]

Originally Posted by EdH

I have a script that will run a whole table against current sequences checking for merges. I'll run it on all the new tables and see what it turns up. At that point there will be a list that can be referenced instead of digging through posts. I'll try to have that later today.

Note that it uses the 80 digit file, so it won't pick up those few merges we found that are outside that.

OK, many thanks for your help, because I don't have a script : I look for the mergers manually and it can take a long time !
Does it use my 80 digit file, on my website ?
Because I know that I will also have to update this file : in a year, things move because of the sequences which merge and which end !
And I hope that when I scan the over 27,000 sequences in the main project, I won't find any broken aliquot sequences !

[EdH]

Originally Posted by garambois

OK, many thanks for your help, because I don't have a script : I look for the mergers manually and it can take a long time !
Does it use my 80 digit file, on my website ?
Because I know that I will also have to update this file : in a year, things move because of the sequences which merge and which end !
And I hope that when I scan the over 27,000 sequences in the main project, I won't find any broken aliquot sequences !

Yes, it uses your 80 digit file (currently the 2020 version). My script still has the i0/i1 error, so I have to remember to manually check those, but the others "seem" to be correct when I do spot checks. I, too, hope this year brings a set with no broken sequences.

I have some expansion to do with my script, so I can call it easier and I need to address the i0/i1 error. At some point, if I get it working the way I'd like, I'll post it here. It's a simple Bash script that runs on one of my RPi machines.

Here are some runs for today:

Running base 37: 
37^6:i126 merges with 109920:i1275 
37^8:i151 merges with 1632:i37 
37^12:i1057 merges with 10824:i28 
37^18:i1430 merges with 3366:i2 
37^22:i519 merges with 1567300:i0   (*Manually fixed*)
37^30:i1193 merges with 35856:i3 
Done in 221 seconds. 
 
Running base 41: 
41^4:i66 merges with 36468:i17 
41^32:i386 merges with 271980:i46 
Done in 108 seconds.
 
Running base 43: 
43^16:i204 merges with 1299520:i4 
43^34:i639 merges with 5208:i10 
Done in 109 seconds.

Running base 450:
Done in 24 seconds.

Running base 882:
Done in 19 seconds.

Running base 33550336:
Done in 34 seconds.

[RichD]

Originally Posted by EdH

I have a script that will run a whole table against current sequences checking for merges. I'll run it on all the new tables and see what it turns up. At that point there will be a list that can be referenced instead of digging through posts. I'll try to have that later today.

Note that it uses the 80 digit file, so it won't pick up those few merges we found that are outside that.

@EdH: You can include base 43 in your script. All exponents (up to 77) are initialized but not ready to be inserted in the master table.

Edit: Oops, late to party for posting...