Aliquot sequences that start on the integer powers n^i

[EdH]

Originally Posted by RichD

I think 31^36 may have merged.

Found:

31^36:i2015 merges with 3762570:i457

Not found earlier because it is above Jean-Luc's C80 listing.

[unconnected]

Please reserve base 79 for me.

[garambois]

Originally Posted by EdH

Found:

31^36:i2015 merges with 3762570:i457

Not found earlier because it is above Jean-Luc's C80 listing.

Please, how could you find this

[garambois]

Originally Posted by unconnected

Please reserve base 79 for me.

OK, thank you very much ! It will be done at the next update next weekend...

[RichD]

It appears 29^50 may have merged.

[EdH]

Originally Posted by RichD

It appears 29^50 may have merged.

 29^50:i1210 merges with 9999286:i5

But, there are many other merges (due to it terminating with a large number of small terms) and I don't know which to treat as the lowest.

Originally Posted by garambois

Please, how could you find this

I wrote a script to work its way back through an Aliquot sequence via the factordb, identifying terms that have more than one source. The "More information" for Aliquot composite terms includes any previous composite Aliquot terms that result in that Aliquot sum. In the above example for RichD, if you look at "More information" for 2409946:

Others:
Aliquot sequence: 3012410
Aliquot sequence: 3340358

you can see two sources. By following the sources, you can reach a first term.

Unfortunately, my script also tends to crash the computer it is run on and I had some LAN trouble at the same time. Coincidence? Which preceded which? No answers. But I don't want to post the script due to the crashes.

[EdH]

Originally Posted by EdH

 29^50:i1210 merges with 9999286:i5

But, there are many other merges (due to it terminating with a large number of small terms) and I don't know which to treat as the lowest.
. . .

In the case of open sequences, the lowest starting term is considered the sequence into which others merge. What determines the sequence into which others merge for terminated sequences? Is it the lowest untouchable sequence or is it the terminating prime?

[Happy5214]

Originally Posted by EdH

In the case of open sequences, the lowest starting term is considered the sequence into which others merge. What determines the sequence into which others merge for terminated sequences? Is it the lowest untouchable sequence or is it the terminating prime?

Personally, I would skip describing the merge and just say it terminates at the prime/cycle. I don't think there's a satisfactory way to describe such a large number of merges in as quick a succession as that.

[EdH]

Originally Posted by Happy5214

Personally, I would skip describing the merge and just say it terminates at the prime/cycle. I don't think there's a satisfactory way to describe such a large number of merges in as quick a succession as that.

That sounds OK, but for 29^50, it merged with something to take it to termination. I guess that it can still be left as just 29^50 terminated.

[EdH]

The base 98 table should all be green at next update.

[garambois]

Originally Posted by EdH

 29^50:i1210 merges with 9999286:i5

But, there are many other merges (due to it terminating with a large number of small terms) and I don't know which to treat as the lowest.


I wrote a script to work its way back through an Aliquot sequence via the factordb, identifying terms that have more than one source. The "More information" for Aliquot composite terms includes any previous composite Aliquot terms that result in that Aliquot sum. In the above example for RichD, if you look at "More information" for 2409946:

Others:
Aliquot sequence: 3012410
Aliquot sequence: 3340358

you can see two sources. By following the sources, you can reach a first term.

Unfortunately, my script also tends to crash the computer it is run on and I had some LAN trouble at the same time. Coincidence? Which preceded which? No answers. But I don't want to post the script due to the crashes.

Thanks Edwin for these explanations !