mersenneforum.org Aliquot sequences that start on the integer powers n^i
 Register FAQ Search Today's Posts Mark Forums Read

 2021-06-07, 13:02 #1145 Happy5214     "Alexander" Nov 2008 The Alamo City 2·3·109 Posts Because it's cheap and can be done quickly using FactorDB, I checked all of the trivial sequences for every number below 20k from the 5- and 28-cycles (including the whole 5-cycle) up to i=12. There were no cycles found other than the one I already mentioned. Last fiddled with by Happy5214 on 2021-06-07 at 13:02
2021-06-07, 17:37   #1146
garambois

"Garambois Jean-Luc"
Oct 2011
France

61110 Posts

Quote:
 Originally Posted by Happy5214 Because it's cheap and can be done quickly using FactorDB, I checked all of the trivial sequences for every number below 20k from the 5- and 28-cycles (including the whole 5-cycle) up to i=12. There were no cycles found other than the one I already mentioned.
This does not surprise me at all, endings of sequences on cycles are very rare, unfortunately.
I will also make some tests of this kind in the next time...

Quote:
 Originally Posted by Happy5214 My point in the post you linked was more along the lines of "they should be alike". With the table now being full-width, there's a ton of empty space, even on my 1600×900 monitor. Perhaps, if it's not too hard, we could add a toggle (a checkbox or a button) that switches between the default view and an "expanded" view that replaces the open columns (or adds to them) with <120, 120-140, and >140 columns.
I hear that idea, but I propose that we work with the page as it is now for a few weeks.
That way, we'll have more time to see if we want to change anything or add more statistics, and if so, what.
Then we will all be able to tell if we are missing columns to do our job.
This does not mean that we forget your idea, but that we may still be waiting for more to come in and then sort out what will be most relevant and see what is feasible without too much difficulty.
Let's take some time to look at different possibilities.
I say all of this because I also have ideas that arise in my mind and I haven't really examined them closely to assess their relevance.
Does this seem right to you ?

2021-06-08, 00:41   #1147
Happy5214

"Alexander"
Nov 2008
The Alamo City

2×3×109 Posts

Quote:
 Originally Posted by garambois Then we will all be able to tell if we are missing columns to do our job.
I can tell you one immediate use (for me at least) for the <120 column. Before my recent forays into initializing bases, my primary focus was finishing off yoyo downdriver runs, and seeing a 0 in a <120 column would allow me to skip checking that base, saving me time. (While it may have a downdriver, it's not low enough to take over yet.)

 2021-06-09, 06:29 #1148 Happy5214     "Alexander" Nov 2008 The Alamo City 65410 Posts 12496 is initialized to 100 digits, and the trivial sequences are done to 120 digits (i=28). I'm going to attempt i=30 and 32, assuming they fit in my 120-digit cofactor limit. The most interesting thing was a non-trivial termination (at a prime) of i=19.
2021-06-09, 09:01   #1149
Happy5214

"Alexander"
Nov 2008
The Alamo City

2×3×109 Posts

Quote:
 Originally Posted by Happy5214 12496 is initialized to 100 digits, and the trivial sequences are done to 120 digits (i=28). I'm going to attempt i=30 and 32, assuming they fit in my 120-digit cofactor limit. The most interesting thing was a non-trivial termination (at a prime) of i=19.
i=30 was terminated (prime), and i=32 hit a 129-digit cofactor and was not finished. I'm done with this base. I'll start base 40 either Wednesday or Thursday (Thursday is more likely, as I have some GIMPS work to catch up on), unless you have another high-priority base to initialize. I assume these sociable cycle bases are now considered a dead end for you given my FactorDB work?

 2021-06-09, 23:34 #1150 VBCurtis     "Curtis" Feb 2005 Riverside, CA 483310 Posts Please update 13^54 and 13^70. My quest to pink-ify base 13 continues.
 2021-06-10, 08:53 #1151 kar_bon     Mar 2006 Germany 13×223 Posts 50^96 terminated
 2021-06-10, 20:39 #1152 garambois     "Garambois Jean-Luc" Oct 2011 France 26316 Posts Page updated. Thanks to all for your help. Now we have 78 bases and several cells have turned green and pink ! Added bases : 39, 12496, 14316 A merger : 47^97:i106 = 23670 = 1134:i9 Attributions : I don't know who did the calculations for 62^80 ? Thank you all for checking if everything is correct for your calculations. Because I made the update very quickly and I did not check everything in detail... Indeed, for the base 14316 which is not a perfect number, we have a cycle of length 28 (exponent 1) and a cycle of length 1 (exponent 10). This is notable ! We were looking for such a base, because it confirms that this is not the case only for bases which are perfect numbers.
2021-06-10, 21:01   #1153
RichD

Sep 2008
Kansas

D2116 Posts

Quote:
 Originally Posted by garambois Attributions : I don't know who did the calculations for 62^80 ?
I finished it off. I see there are still outstanding exponents from base 62 I did not consider. That is why base 74 is slow going, along with part-time work on another project.

2021-06-11, 00:47   #1154
Happy5214

"Alexander"
Nov 2008
The Alamo City

2×3×109 Posts

Quote:
 Originally Posted by garambois Page updated. Thanks to all for your help. Now we have 78 bases and several cells have turned green and pink ! Added bases : 39, 12496, 14316 A merger : 47^97:i106 = 23670 = 1134:i9 Attributions : I don't know who did the calculations for 62^80 ? Thank you all for checking if everything is correct for your calculations. Because I made the update very quickly and I did not check everything in detail...
There were two unlisted merges for base 39 that I forgot to report:
Code:
39^4:i67 merges with 3876:i5
39^40:i1167 merges with 42024:i5

2021-06-11, 04:11   #1155
Happy5214

"Alexander"
Nov 2008
The Alamo City

2·3·109 Posts

I updated the conjectures page to add some of the more trivial proofs. Specifically, I added proofs for index 1 conjectures for bases 2, 3, and 5, which all use algebraic factors. You could probably use that template and FactorDB to fill in the rest of the index 1 conjecture proofs for the remaining prime bases (the composite ones will be harder).
Attached Files
 conjectures.tar.gz (6.2 KB, 8 views)

 Similar Threads Thread Thread Starter Forum Replies Last Post fivemack FactorDB 46 2021-02-21 10:46 schickel FactorDB 18 2013-06-12 16:09 garambois Aliquot Sequences 34 2012-06-10 21:53 Andi47 FactorDB 21 2011-12-29 21:11 schickel mersennewiki 0 2008-12-30 07:07

All times are UTC. The time now is 19:29.

Sat Jun 19 19:29:35 UTC 2021 up 22 days, 17:16, 0 users, load averages: 3.59, 2.98, 2.77