20210607, 13:02  #1145 
"Alexander"
Nov 2008
The Alamo City
2·379 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 28cycles (including the whole 5cycle) up to i=12. There were no cycles found other than the one I already mentioned.
Last fiddled with by Happy5214 on 20210607 at 13:02 
20210607, 17:37  #1146  
"Garambois JeanLuc"
Oct 2011
France
7×97 Posts 
Quote:
I will also make some tests of this kind in the next time... Quote:
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 ? 

20210608, 00:41  #1147 
"Alexander"
Nov 2008
The Alamo City
2×379 Posts 
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.)

20210609, 06:29  #1148 
"Alexander"
Nov 2008
The Alamo City
2·379 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 120digit cofactor limit. The most interesting thing was a nontrivial termination (at a prime) of i=19.

20210609, 09:01  #1149 
"Alexander"
Nov 2008
The Alamo City
2×379 Posts 
i=30 was terminated (prime), and i=32 hit a 129digit 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 highpriority base to initialize. I assume these sociable cycle bases are now considered a dead end for you given my FactorDB work?

20210609, 23:34  #1150 
"Curtis"
Feb 2005
Riverside, CA
2^{7}×3×13 Posts 
Please update 13^54 and 13^70.
My quest to pinkify base 13 continues. 
20210610, 08:53  #1151 
Mar 2006
Germany
5553_{8} Posts 
50^96 terminated

20210610, 20:39  #1152 
"Garambois JeanLuc"
Oct 2011
France
7·97 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. 
20210610, 21:01  #1153 
Sep 2008
Kansas
5·13·53 Posts 

20210611, 00:47  #1154  
"Alexander"
Nov 2008
The Alamo City
2F6_{16} Posts 
Quote:
Code:
39^4:i67 merges with 3876:i5 39^40:i1167 merges with 42024:i5 

20210611, 04:11  #1155 
"Alexander"
Nov 2008
The Alamo City
2·379 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).

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