Aliquot sequences that start on the integer powers n^i

[EdH]

103^26:i5766 merges with 247212:i17.

This one's graph is quite a rugged terrain.

[gd_barnes]

Originally Posted by garambois

Small update done on the page.
Thanks to all for your help.

4 errors pointed out by Karsten corrected, thanks to him.
Bases 103, 313 and 47616 updated, thanks to Gary and Edwin.

I really would have bet that we would have sequence endings for base 313, even an ending on a cycle !

You updated a few hours too early. When updated, base 313 was down to 2 sequences remaining to have all at >= 120 digits.

Now base 313 is complete to >= 120 digits. :-)

I'm a little confused on why having 2 or more sequences terminate in a cycle for a base would predict additional terminations for a base, whether they be cycle or otherwise. It seems there is much randomness in all sequences after small factors work their way through the first few indexes. It seems like trying to predict where a huge prime will occur.

Regardless, I'm still happy to search things on the offhand chance that such patterns can be found.

[gd_barnes]

317^8 merges at index=2830 with 36468:i22.

Now 4 terminations and 2 merges for the 120-digit effort.

[garambois]

Originally Posted by gd_barnes

I'm a little confused on why having 2 or more sequences terminate in a cycle for a base would predict additional terminations for a base, whether they be cycle or otherwise. It seems there is much randomness in all sequences after small factors work their way through the first few indexes. It seems like trying to predict where a huge prime will occur.

Regardless, I'm still happy to search things on the offhand chance that such patterns can be found.

There is no possible prediction.
I just find it very surprising that for all the bases that are prime numbers, there are only endings of sequences on cycles of the same length.
And as I suppose that this is a coincidence, I would like to confirm it by finding for example for the base 313 an end of sequence on a cycle of length other than 2.
This is the expected result : randomness.

[EdH]

Another:

103^40:i1329 merges with 27916:i5

BTW, Jean-Luc, I just thought I'd mention that I'm using your latest OE_3000000_C80.txt to find these. Thanks!

[yoyo]

Is base 88 still reserved? It would be the next on my list to take.
Otherwise I take 89 and following bases.
I need more food for my volunteers ;)

[garambois]

Originally Posted by EdH

BTW, Jean-Luc, I just thought I'd mention that I'm using your latest OE_3000000_C80.txt to find these. Thanks!

Great !
It is much better to use the latest version, even if the probability of error remains low with the old version, it is not zero.

Originally Posted by yoyo

Is base 88 still reserved? It would be the next on my list to take.
Otherwise I take 89 and following bases.
I need more food for my volunteers ;)

Excellent !
Base 88 is always reserved.
So I reserve base 89 for you and the following ones (opposite parities).
Up to which base do you want to reserve ?

[yoyo]

I'll take bases 89 90 91 92 93 94.

[Sergiosi]

I have found the downdriver on 92^61 just this morning.


@yoyo: could you please leave this sequence to me?

[yoyo]

Yes, let this sequence stay at your side.
I'll take additionally 95 96 97 99.

[EdH]

Base 103 is completed - all opens >=120 digits.