20200824, 19:47  #496 
"Ed Hall"
Dec 2009
Adirondack Mtns
4,001 Posts 
Here's a full list of all the terminating primes from all the sequences across all the tables on the page. I also added base 79 through power 79 since it's ready to add to the page. There are 1692 unique terminating primes found to this date.
I still haven't solved the exponent sorting, but the bases should be sorted. 
20200825, 01:39  #497 
"Ed Hall"
Dec 2009
Adirondack Mtns
FA1_{16} Posts 
Although they are there for further, they are still missing after a point. I am trying to find out why, but not getting anywhere, yet. Oddly they stop during the 601 prime, at the line right after the 601 line of the document.

20200825, 02:04  #498 
"Ed Hall"
Dec 2009
Adirondack Mtns
4,001 Posts 
Alright! I found the culprit. I think this document will be complete. The 601 was a subtle indicator  an easy fix after all, once I realized the real problem.

20200825, 02:32  #499 
Sep 2008
Kansas
3^{2}×383 Posts 
Table n=20 will be ready to insert about the time the next update is due to be posted.

20200825, 09:39  #500 
"Garambois JeanLuc"
Oct 2011
France
7·97 Posts 
@EdH : Many thanks to you. The table is perfect. All I have to do now is to do by hand, the last sort in ascending order of exponents, while waiting to write my own program that will give the same output.
But for the moment at the sight of this table, it does not seem to appear of new conjecture ! Unfortunately, the start of the school year is fast approaching and I would have less time to work on on the aliquot sequences ! @RichD : Thanks a lot. I don't think I'll do an update until next weekend. I will then add bases 79 and 20... 
20200825, 10:50  #501 
"Garambois JeanLuc"
Oct 2011
France
7×97 Posts 
About the search for possible OpenEnd sequences among those that should end trivially
The sequences we have calculated so far that end trivially are those of bases 2, 18 and those beginning with b^i with b (base) and i (exponent) of the same parity. For all these sequences, at the first iteration, we get an odd number. This is what makes them end. All the following terms remain essentially odd, with rare exceptions where we always end up with an odd number. For one of these aliquot sequence to be OpenEnd, one of its odd terms would have to be an aliquot antecedent of an even OpenEnd aliquot sequence, which we are familiar with in the main project. Let me give you the following two facts, and after, draw the conclusions : 1) At the last update on August 21, 2020, in our project, we had calculated 1827 sequences that ended trivially. 2) Using my fundamental database, I determined the following :  There are 4 odd numbers less than 10,000 which are the start of OpenEnd sequences (3025, 7225, 8015 and 8427)  There are 80 odd numbers less than 100,000 which are the start of OpenEnd sequences.  There are 810 odd numbers less than 1,000,000 which are the start of OpenEnd sequences.  There are 7734 odd numbers less than 10,000,000 which are the start of OpenEnd sequences. In fact, these numbers are a bit too big, because in my fundamental database, a sequence is OpenEnd as soon as its terms reach 50 digits. But the order of magnitude is there: out of all the odd numbers, there is 1 in 1300 or even say 1 in 2000, which is the start of an OpenEnd sequence. Taking into account these two facts, and as in a sequence, one "picks" an odd number at each iteration, I ask the question that causes me so much trouble : Why hasn't an OpenEnd sequence been found yet among those that must end trivially ? Last fiddled with by EdH on 20200825 at 13:14 Reason: See next post. 
20200825, 12:30  #502 
"Garambois JeanLuc"
Oct 2011
France
679_{10} Posts 
Please, on the previous post, I spotted an error and I can no longer correct myself !
Code:
 There are 810 odd numbers less than 100,000 which are the start of OpenEnd sequences.  There are 7734 odd numbers less than 1,000,000 which are the start of OpenEnd sequences. In fact, these numbers are a bit too big, because in my fundamental database, a sequence is OpenEnd as soon as its terms reach 50 digits. But the order of magnitude is there: out of all the odd numbers, there is 1 in 130 or even say 1 in 200, which is the start of an OpenEnd sequence. Code:
 There are 810 odd numbers less than 1,000,000 which are the start of OpenEnd sequences.  There are 7734 odd numbers less than 10,000,000 which are the start of OpenEnd sequences. In fact, these numbers are a bit too big, because in my fundamental database, a sequence is OpenEnd as soon as its terms reach 50 digits. But the order of magnitude is there: out of all the odd numbers, there is 1 in 1300 or even say 1 in 2000, which is the start of an OpenEnd sequence. 
20200825, 17:30  #503 
"Garambois JeanLuc"
Oct 2011
France
7×97 Posts 
Thank you so much Ed !

20200825, 19:41  #504 
Oct 2006
Berlin, Germany
2×313 Posts 
I take base 12.
Do I take too much? On base 13 are some reservations. 
20200825, 19:51  #505 
"Curtis"
Feb 2005
Riverside, CA
2·11·227 Posts 
I've been working on base 13 for a few years, and prefer to work only on base 13. Please skip that one!

20200825, 20:30  #506 
"Ed Hall"
Dec 2009
Adirondack Mtns
4,001 Posts 
OK! I think I have them all sorted correctly, now. Attached is a new document with bases AND powers sorted (and, the power expansion is to the end).

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