Aliquot sequences that start on the integer powers n^i

[VBCurtis]

I'd like to handle base 800.

[garambois]

Originally Posted by VBCurtis

I'd like to handle base 800.

OK, perfect.
Many thanks !

[RichD]

I'll start on base 722.

[Happy5214]

Originally Posted by Happy5214

Base 48 is done. I got to i=80 on the trivial sequences (135 digits). Base 24 is also done to i=50. If nobody reserves the priority cycle bases by the time I finish my catch-up with GIMPS, I may take one or both of those.

Scratch that, base 48 is not done. I misread my own notes in my recent confusion. Only the trivial sequences are done. I'm expediting the non-trivial sequences, and I hope to have them done by Thursday.

[bur]

Then I'll get on to initializing 2 * 18^2 = 648 when I'm finished with base 53 trivials.

[garambois]

Many thanks to all.
Yes, thursday I will do a complete update.

[Happy5214]

Originally Posted by Happy5214

Scratch that, base 48 is not done. I misread my own notes in my recent confusion. Only the trivial sequences are done. I'm expediting the non-trivial sequences, and I hope to have them done by Thursday.

OK, now base 48 is ready. The non-trivial sequences have been done to 100 digits. That went more quickly than I was expecting.

[Happy5214]

It appears someone already did base 14288 below i=18 up to around 100 digits without reserving it (unless I missed it) and posted the results yesterday to FactorDB. Whoever did that should have just reserved the base officially for initialization, since I was waiting to see if anyone else wanted it before I reserved it. I guess I'll finish what's left.

[bur]

All trivial sequences of base 53 for i < 99 are terminated. Just 53^99 is stubborn, it has 3^2 * 5 factors and decreases very slowly. Now at i12 it's a c164 co-factor. It'll take about a week to factor and before the sequence terminates I guess some more will follow.

All non-trivials are done to 110 digits at least.

Since you said that yoyo (is that yoyo@home?) will pick up the non-trivials sooner or later I guess it makes more sense to begin base 2*18^2 instead of continuing with base 53?

[RichD]

Base 722 can be added at the next update.

[Happy5214]

Originally Posted by bur

Since you said that yoyo (is that yoyo@home?) will pick up the non-trivials sooner or later I guess it makes more sense to begin base 2*18^2 instead of continuing with base 53?

Confusingly, it's actually yafu@home, but yoyo is the forum user who manages it. I think yafu@home and the actual yoyo@home are both under the Rechenkraft.net umbrella, so they're basically sister projects.

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Edit: Base 14288 initialization is done. I got lucky with i=34 with a 26-digit smallest factor on the first term that knocked the sequence below 120 digits, but not so lucky for i=32 (which was not completed). Other than non-trivial terminations (at primes) of i=3, 7. and 9, there was nothing else interesting with this base. Base 19116 is next, and I'll try to get as many trivial sequences done as possible before the update.