20210802, 13:29  #1266 
"Rich"
Aug 2002
Benicia, California
2^{3}·3·5·11 Posts 
392^55 terminates P3 at i94.

20210803, 07:43  #1267  
"Garambois JeanLuc"
Oct 2011
France
647 Posts 
Quote:
I understand that your criteria make you handle sequences that are not taken into account by our project page. If you handle base 288 with exponents > 60, it raises the question for me : Do you think I should extend all bases < 1000 to exponent 70 on the project page ? Please give me your opinions on this question, because the limit exponents I chose are not a rigorous choice. For example for base 999, we have 999^70 which has 210 digits ! It's just to avoid nonsense. I can't put 8128^100 on the page, because that number has 391 digits ! 

20210803, 08:29  #1268  
"Garambois JeanLuc"
Oct 2011
France
647 Posts 
Quote:
This happens for all bases. Reminder :  Sequences whose bases and exponents have the same parity usually terminate trivially (the only exception currently known : 29^15).  Sequences whose bases and exponents do not have the same parity end very rarely.  For bases that are doubles of squares, all sequences end trivially in general (no exception known at the moment). This is due to a theorem that says that in a sequence, there is a change of parity only when a term is a perfect square or the double of a perfect square. And in general, when we have odd terms in a sequence, it ends quickly. 

20210803, 08:51  #1269  
"Garambois JeanLuc"
Oct 2011
France
647 Posts 
Quote:
Honestly, I am against this idea. Indeed, if Catalan's conjecture is true, then the sequences of the main project will all come out of the main project one day. The placement of a base in this hypothetical new category would therefore be in no way final, unlike the placements of bases in all our other current categories. But I agree that creating a category for the OpenEnd bases of the main project would facilitate the statistics ! Because, in the other hand, it is very interesting indeed to calculate the sequences of the bases in the main project. I had already noticed that for the Lehmer five, nontrivial sequences ending seemed to be very rare. But I think this must be a coincidence. Otherwise, we would have a very curious conjecture ! It's a great idea to dig into this question ! 

20210803, 09:01  #1270  
"Garambois JeanLuc"
Oct 2011
France
647 Posts 
Quote:
Let me know if you manage to initialize bases with the minimum rules we set : for a given base, compute all sequences <120 digits that end trivially and <100 digits that are OpenEnd. These are only the minimal rules, you can do more if you have big computational resources ;) 

20210803, 09:44  #1271  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
2^{3}×5×73 Posts 
Quote:


20210803, 13:55  #1272  
Oct 2006
Berlin, Germany
623_{10} Posts 
Quote:


20210803, 15:10  #1273 
"Garambois JeanLuc"
Oct 2011
France
647 Posts 
Page updated.
Many thanks to all for your help ! Please let me know if you notice any errors. Added bases : 14264, 14536, 15472 (C5 cycle completed !). New bases reserved by yoyo : 39, 40, 44, 48, 50, 53, 62, 74, 162, 211, 722, 882. Several terminated sequences of other bases with attribution. I will be able to start doing the first data analysis tests of the project later this week... OK, Thank you for your answer. Thanks ! The reservations on the page will be effective only when the base will be initialized. 
20210803, 18:07  #1274 
Sep 2008
Kansas
2^{2}×7×11^{2} Posts 
Looks like somebody might need more numbers to factor. I'll initialize bases 52, 54 & 55 next.

20210803, 21:55  #1275 
"Rich"
Aug 2002
Benicia, California
2^{3}×3×5×11 Posts 
392^57 terminates P42 at i27.
392^59 terminates P34 at i84. 
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