Aliquot sequences that start on the integer powers n^i - Page 122

garambois · 2021-08-21, 08:13

Quote:

Originally Posted by yoyo

I'll take bases 276, 552 and 966.

Reservation and update made for these 3 bases.
Thank you very much, I will follow the evolution of the calculations with great attention.

garambois · 2021-08-21, 08:53

@bur and VBCurtis :

Thank you very much for your positive messages.
I think you are right and that we should see the project as you say.
All our calculations for this project will be at least as useful as others anyway, given the important role that integer powers play in number theory.
And I've said it all along : I didn't know if the data analyses would yield interesting results.
I was not intending to stop the project, but as you say, rather to take a break from data analysis.
If there is a general law to observe, it must be much more complicated than I could have imagined.
And if any of us were to find this law by observing the tables attached in my post #1328, then, we would be taking a giant step forward in the knowledge of aliquot sequences.
But maybe this law does not exist.
Or maybe we are missing some data. But what we are missing is rather larger exponents for each basis, that is my hunch. And we all know that it is impossible to increase the number of exponents for the bases.
But it is likely that in the future I will have to look at the data forgetting the original reason for creating the project.
There must be a lot of other interesting things to discover (or not !).

So let's get on with our calculations, all those who like it.
And when our intuition tells us it's time, maybe we'll look at the data again and notice some interesting things because of those calculations !

Happy5214 · 2021-08-21, 09:08

I'm flattered, but 276^70 should be marked Anonymous. I didn't even explore above i=60 for any of the Lehmer five bases. It was probably your page-generating script that finished it off.

I've never been in this project for the conjectures, to be honest (other than fixing up your webpage). For me, it's all about the sequences being easier to work on than the main project, and filling in gaps to make the tables more complete. Keep shooting for the stars! We never know we'll find.

RichD · 2021-08-21, 12:07

Terminates:
54^70
54^72
55^73

garambois · 2021-08-22, 16:06

Quote:

Originally Posted by Happy5214

I'm flattered, but 276^70 should be marked Anonymous. I didn't even explore above i=60 for any of the Lehmer five bases. It was probably your page-generating script that finished it off.

OK thanks.
Next update I'll put this sequence as calculated by an anonymous person.

Quote:

Originally Posted by Happy5214

Keep shooting for the stars! We never know we'll find.

You can trust me for that !

Quote:

Originally Posted by RichD

Terminates:
54^70
54^72
55^73

OK thanks.
This will be taken into account in the next update.

RichD · 2021-08-24, 11:12

Terminates:
52^76
54^74
54^76
55^75

This concludes my work on these tables.

I'll start on bases 56, 57,59 and 60.

unconnected · 2021-08-27, 09:37

79^89 terminates!
BTW, I'm working on base 79 (odd n) up to 101.

garambois · 2021-08-29, 09:31

OK, I'm back from a few days of vacation.

Quote:

Originally Posted by RichD

Terminates:
52^76
54^74
54^76
55^75

This concludes my work on these tables.

I'll start on bases 56, 57,59 and 60.

Thank you very much for this work.
The finished sequences will be taken into account in the next update.
For the initializations of the new bases, excellent !
Let me know when I should add them to our page.

Quote:

Originally Posted by unconnected

79^89 terminates!
BTW, I'm working on base 79 (odd n) up to 101.

Thank you very much !
Reservations will be noted in the next update.
You want to do the calculations for the odd exponents up to 99, right (and not 101 which is not on the page ?) ?

unconnected · 2021-08-29, 14:58

Quote:

Originally Posted by garambois

You want to do the calculations for the odd exponents up to 99, right (and not 101 which is not on the page ?) ?

Yes.

garambois · 2021-08-29, 15:44

WOW, OK, so good luck, because the calculations will be very long, a record for the project !
Several sequences exceed 170 digits !
79^93 and 79^99 will be formidable, as the terms have the factor 3.

RichD · 2021-08-31, 22:25

Base 56 can be added at the next update.

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2021-08-21, 08:53	#1333
garambois "Garambois Jean-Luc" Oct 2011 France 5·7·23 Posts	@bur and VBCurtis : Thank you very much for your positive messages. I think you are right and that we should see the project as you say. All our calculations for this project will be at least as useful as others anyway, given the important role that integer powers play in number theory. And I've said it all along : I didn't know if the data analyses would yield interesting results. I was not intending to stop the project, but as you say, rather to take a break from data analysis. If there is a general law to observe, it must be much more complicated than I could have imagined. And if any of us were to find this law by observing the tables attached in my post #1328, then, we would be taking a giant step forward in the knowledge of aliquot sequences. But maybe this law does not exist. Or maybe we are missing some data. But what we are missing is rather larger exponents for each basis, that is my hunch. And we all know that it is impossible to increase the number of exponents for the bases. But it is likely that in the future I will have to look at the data forgetting the original reason for creating the project. There must be a lot of other interesting things to discover (or not !). So let's get on with our calculations, all those who like it. And when our intuition tells us it's time, maybe we'll look at the data again and notice some interesting things because of those calculations !

2021-08-21, 09:08	#1334
Happy5214 "Alexander" Nov 2008 The Alamo City 2⁵·5² Posts	I'm flattered, but 276^70 should be marked Anonymous. I didn't even explore above i=60 for any of the Lehmer five bases. It was probably your page-generating script that finished it off. I've never been in this project for the conjectures, to be honest (other than fixing up your webpage). For me, it's all about the sequences being easier to work on than the main project, and filling in gaps to make the tables more complete. Keep shooting for the stars! We never know we'll find.

2021-08-21, 12:07	#1335
RichD Sep 2008 Kansas 110111101011₂ Posts	Terminates: 54^70 54^72 55^73

2021-08-24, 11:12	#1337
RichD Sep 2008 Kansas 7·509 Posts	Terminates: 52^76 54^74 54^76 55^75 This concludes my work on these tables. I'll start on bases 56, 57,59 and 60.

2021-08-27, 09:37	#1338
unconnected May 2009 Russia, Moscow ACC₁₆ Posts	79^89 terminates! BTW, I'm working on base 79 (odd n) up to 101.

2021-08-29, 15:44	#1341
garambois "Garambois Jean-Luc" Oct 2011 France 805₁₀ Posts	WOW, OK, so good luck, because the calculations will be very long, a record for the project ! Several sequences exceed 170 digits ! 79^93 and 79^99 will be formidable, as the terms have the factor 3.

2021-08-31, 22:25	#1342
RichD Sep 2008 Kansas 7×509 Posts	Base 56 can be added at the next update.