Aliquot sequences that start on the integer powers n^i - Page 65

garambois · 2020-12-25, 18:30

OK, base 439 complete.
A lot of thanks.
Merry Christmas to you too and to all of you !

garambois · 2020-12-27, 10:37

OK, page updated.
Many thanks to all for your contribution !

Base 200 added up to exponent 54.
Base 288 added up to exponent 50.
10^129 merge added.
Base 439, work completed.
Addition of exponents 64 to 95 for base 79.

I still have to correct some attributions for base 288, at the next update...

There are now a total of 45 bases on the page !

EdH · 2020-12-27, 16:04

Quote:

Originally Posted by garambois

. . .
There are now a total of 45 bases on the page !

And, if my count is correct, 4618 sequences. . .

garambois · 2020-12-30, 09:16

Your addition is correct, I find the same. And I also added the other columns, it gives :

All : 4618
Done : 2986
Open : 1608
Merges : 78
Cycle : 24

And we have the exact addition : 24 + 1608 + 2986 = 4618

Note that 24 + 2986 = 3010.
So we have 3010 / 4618 = 0.6518 or about 65% of all our aliquot sequences for which we have finished the caculs !

RichD · 2020-12-30, 10:59

29^36 terminates.

garambois · 2020-12-30, 19:00

Waouh : a non-trivial ending !
Congratulations !

29^15 is also to my knowledge the only aliquot sequence in our project that should end trivially and that doesn't ! At index 36, we find a perfect square term. So we have a change of parity. And we have at index 37 the number 18528 which is the start of an Open-End sequence.

garambois · 2021-01-17, 20:04

OK, page updated.
Many thanks to all for your help !

Notable discovery for this time :
The sequence 3^286 ends with the 28-cycle.
- This is the first sequence of the project that ends on the 28-cycle !
- And it is the first sequence that ends on a cycle for base 3 !
- And we hadn't had any sequence that ended with a cycle of length other than 1 or 2 before that in this project !
Karsten Bonath had flair in pushing further the calculations for this sequence !
Congratulations !

Now, let's wait to find another sequence that ends with a cycle for base 3 to see how long its cycle length will be.

Happy5214 · 2021-01-29, 21:27

After a little more than 4,000 terms and a heart-stopping roller-coaster ride in the middle, my run with 24^21 ends with nothing to show for it.

There are a couple of glaring holes in the list, bases 22 and 26. I'd like to initialize those to 100 digits. The even exponents are already done for both up to 120 digits.

Also, would it be too much trouble to generate a page like http://www.aliquotes.com/OE_3000000_C80.txt for the power sequences?

Happy5214 · 2021-01-30, 07:23

Base 26 is done to 100 digits (26^69). There were 3 merges (26^15:i350 = 2360:i4, 26^35:i503 = 87612:i4, and 26^55:i458 = 871000:i0), plus 26^67, which had additional terms already in FactorDB that I didn't compute, but I couldn't deduce a merge for. Exponents 1, 3, 5, 19, 31, 33, and 59 terminate. I'll start base 22 next.

garambois · 2021-01-30, 15:36

OK, page updated.
Thanks to all for your help !

Quote:

Originally Posted by Happy5214

After a little more than 4,000 terms and a heart-stopping roller-coaster ride in the middle, my run with 24^21 ends with nothing to show for it.

OK, thanks !

Quote:

Originally Posted by Happy5214

There are a couple of glaring holes in the list, bases 22 and 26. I'd like to initialize those to 100 digits. The even exponents are already done for both up to 120 digits.
...
...
Base 26 is done to 100 digits (26^69). There were 3 merges (26^15:i350 = 2360:i4, 26^35:i503 = 87612:i4, and 26^55:i458 = 871000:i0), plus 26^67, which had additional terms already in FactorDB that I didn't compute, but I couldn't deduce a merge for. Exponents 1, 3, 5, 19, 31, 33, and 59 terminate.

OK, thanks !
Base 26 added.
Congrats on the non-trivial sequences that are coming to an end !
For mergers, I find exactly the same as you.
For 26^67, sorry, but I can't find better than you can of which merger it could be ?
I am waiting to hear from you for base 22.

Yes, there are still holes in the list. At the beginning of the project, we wanted to calculate all the bases up to 100, but when we realized the difficulty of the task, we revised our ambitions downwards !

Quote:

Originally Posted by Happy5214

Also, would it be too much trouble to generate a page like http://www.aliquotes.com/OE_3000000_C80.txt for the power sequences?

This is a good idea.
I will think about it during my next vacations in a few weeks.

RichD · 2021-01-30, 17:35

Would you like table 338 ( 2 * 13^2 ) initialized? Or do you have enough data for 2 * prime^2 to understand the trend? I can start on it if you like.

2020-12-27, 10:37	#706
garambois Oct 2011 715₈ Posts	OK, page updated. Many thanks to all for your contribution ! Base 200 added up to exponent 54. Base 288 added up to exponent 50. 10^129 merge added. Base 439, work completed. Addition of exponents 64 to 95 for base 79. I still have to correct some attributions for base 288, at the next update... There are now a total of 45 bases on the page ! Last fiddled with by garambois on 2020-12-27 at 10:56 Reason: Forgot to mention the addition of exponents for the base 79

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2020-12-25, 18:30	#705
garambois Oct 2011 715₈ Posts	OK, base 439 complete. A lot of thanks. Merry Christmas to you too and to all of you !

2020-12-30, 09:16	#708
garambois Oct 2011 461 Posts	Your addition is correct, I find the same. And I also added the other columns, it gives : All : 4618 Done : 2986 Open : 1608 Merges : 78 Cycle : 24 And we have the exact addition : 24 + 1608 + 2986 = 4618 Note that 24 + 2986 = 3010. So we have 3010 / 4618 = 0.6518 or about 65% of all our aliquot sequences for which we have finished the caculs !

2020-12-30, 10:59	#709
RichD Sep 2008 Kansas 2²·3²·7·13 Posts	29^36 terminates.

2020-12-30, 19:00	#710
garambois Oct 2011 1CD₁₆ Posts	Waouh : a non-trivial ending ! Congratulations ! 29^15 is also to my knowledge the only aliquot sequence in our project that should end trivially and that doesn't ! At index 36, we find a perfect square term. So we have a change of parity. And we have at index 37 the number 18528 which is the start of an Open-End sequence.

2021-01-17, 20:04	#711
garambois Oct 2011 461₁₀ Posts	OK, page updated. Many thanks to all for your help ! Notable discovery for this time : The sequence 3^286 ends with the 28-cycle. - This is the first sequence of the project that ends on the 28-cycle ! - And it is the first sequence that ends on a cycle for base 3 ! - And we hadn't had any sequence that ended with a cycle of length other than 1 or 2 before that in this project ! Karsten Bonath had flair in pushing further the calculations for this sequence ! Congratulations ! Now, let's wait to find another sequence that ends with a cycle for base 3 to see how long its cycle length will be.

2021-01-29, 21:27	#712
Happy5214 "Alexander" Nov 2008 The Alamo City 17×29 Posts	After a little more than 4,000 terms and a heart-stopping roller-coaster ride in the middle, my run with 24^21 ends with nothing to show for it. There are a couple of glaring holes in the list, bases 22 and 26. I'd like to initialize those to 100 digits. The even exponents are already done for both up to 120 digits. Also, would it be too much trouble to generate a page like http://www.aliquotes.com/OE_3000000_C80.txt for the power sequences?

2021-01-30, 07:23	#713
Happy5214 "Alexander" Nov 2008 The Alamo City 17×29 Posts	Base 26 is done to 100 digits (26^69). There were 3 merges (26^15:i350 = 2360:i4, 26^35:i503 = 87612:i4, and 26^55:i458 = 871000:i0), plus 26^67, which had additional terms already in FactorDB that I didn't compute, but I couldn't deduce a merge for. Exponents 1, 3, 5, 19, 31, 33, and 59 terminate. I'll start base 22 next.

2021-01-30, 17:35	#715
RichD Sep 2008 Kansas 2²·3²·7·13 Posts	Would you like table 338 ( 2 * 13^2 ) initialized? Or do you have enough data for 2 * prime^2 to understand the trend? I can start on it if you like.