20200820, 03:45  #452  
Aug 2020
2×3 Posts 
Quote:
Quote:


20200820, 07:05  #453 
Oct 2011
352_{10} Posts 

20200820, 07:13  #454  
Oct 2011
352_{10} Posts 
Quote:
I didn't know the instruction "grep", I'm ashamed ! Thank you for this new tool for me ! The "grep" instruction doesn't give exactly the result I expect but I have no doubt that it will be very useful to me... 

20200820, 07:55  #455 
Oct 2011
160_{16} Posts 
@EdH :
Please, is it possible to modify question 3 of post #447 like this: Code:
Question 3 : How to prove (or invalidate) otherwise than by calculation, this kind of result (conjectures often noted **): If n=3^(78*k), then s(n), s(n) and s(n)) are all three divisible by 79? This kind of proof must be much, much more difficult than the one we are talking about in question 2! Code:
Question 3 : How to prove (or invalidate) otherwise than by calculation, this kind of result (conjectures often noted **): If n=3^(78*k), then s(n), s(s(n)) and s(s(s(n))) are all three divisible by 79? This kind of proof must be much, much more difficult than the one we are talking about in question 2! Machine translation played tricks on me ! But warachwe magnificently anticipated and corrected himself !!! 
20200820, 08:24  #456  
Oct 2011
101100000_{2} Posts 
Quote:
Okay, thank you so much for your help! I suspected this kind of result could be demonstrated. This implies that a large part of my conjectures (almost all those with a star) are in fact proven. Quote:
There was an error in the wording of question 3 of post #447, but you anticipated the real question I wanted to ask... Here again, thank you very much for your help ! I am really very surprised ! I thought that my conjectures noted with two stars implied mechanisms impossible to understand. Your explanations, as well as those of post #452 show that the conjectures noted with two stars are certainly not true, because if we continue the calculations long enough, sooner or later, for a rather large k, for example in the case of 3^(78*k), we will find the factor 157^2 in s(s(n)). These explanations significantly change the order of priorities for the calculations for the rest of the project. Above all, these explanations exempt us from continuing to look for this kind of conjectures. 

20200820, 09:32  #457  
Oct 2011
2^{5}×11 Posts 
What are we going to do now ?
If I take into account the events of the last few days, the study of the occurrences of prime numbers in all the terms of a sequence no longer seems to be a priority. I will tackle this problem in the light of the explanations in post #452. It therefore seems that it will be more useful to focus on the prime numbers that end sequences. We have to try to find at last some conjectures not yet known !!! However, the sequences that we are fairly certain that they end with a prime number are those that begin with numbers n^i when n and i have the same parity. If n and i don't have the same parity, some sequences also end but they are much rarer, but this makes them very interesting. So I propose : 1) To try to continue to advance (or even better, to end) sequences that have orange boxes for the different bases. 2) To start new bases and especially bases that are prime numbers:  Base 18  Base 19  Base 20  Base 23  Base 29  Base 31  Base 79 (seems to play a special role !) 3) To try to extend for each base the number of cells n^i with n and i having the same parity. I think to extend to the next update some bases in the following way : Code:
for base 3 i from 252 to 335 for base 5 i from 172 to 229 for base 6 i from 155 to 206 for base 7 i from 142 to 189 for base 10 i from 121 to 160 for base 11 i from 116 to 153 for base 12 i from 113 to 148 for base 13 i from 108 to 143 for base 14 i from 105 to 140 for base 15 i from 104 to 139 for base 17 i from 98 to 131 Quote:
Is it possible for you (or others who wish to do so) to do the preliminary work for either of the bases presented in point 2) ? @ yoyo : Is it possible for you at first to continue working on the orange cells on base 3? (point 1) above). And if you are willing to devote more computing resources to this project, you can add the orange cells from another base, for example base 5 (especially the cells that are stopped at 120 or 121 digits). Just let me know so that I can note the reservations on the page. With regard to point 3), I know that this request is not popular because it is very resourceintensive. But I think it is an important point. Let's wait until we see the update to get a good visualization of the work to be done. Everyone will then be able to see if they want to start according to their possibilities. 

20200820, 10:59  #458 
Oct 2006
Berlin, Germany
591_{10} Posts 
I ran everything until the remaining composite is greater than C139.
Currently running up to 3^250 and 5^250 Seems that 5^185 5^179 have finished so far. If I need more for my hungry volunteers I would take base 6 and 7. Last fiddled with by yoyo on 20200820 at 11:00 
20200820, 11:25  #459 
Sep 2008
Kansas
2·1,571 Posts 
I will start preliminary work on Base 18 & Base 19. Work will (slowly) continue on Base 770 in the background.

20200820, 11:39  #460  
"Ed Hall"
Dec 2009
Adirondack Mtns
3,389 Posts 
Quote:
@warachwe: May I edit garambois' quote in your post 450 to match the current version in post #447? 

20200820, 12:45  #461 
Sep 2008
Kansas
2·1,571 Posts 
Base 18
Base 18 table is ready for insertion. I took n to 96. Everything n <= 64 terminates (green). n > 64 has remaining composites near C80 or above and will need more work. They are all odd so they most likely will terminate. I will add them to the work queue which includes Base 770.

20200820, 15:33  #462 
"Ed Hall"
Dec 2009
Adirondack Mtns
3,389 Posts 
While we wait for the next update, to get a feel for the work relating to proposition 3, I will do the preliminary work for table 79.

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Broken aliquot sequences  fivemack  FactorDB  45  20200516 15:22 
Broken aliquot sequences  schickel  FactorDB  18  20130612 16:09 
A new theorem about aliquot sequences  garambois  Aliquot Sequences  34  20120610 21:53 
poaching aliquot sequences...  Andi47  FactorDB  21  20111229 21:11 
New article on aliquot sequences  schickel  mersennewiki  0  20081230 07:07 