20200820, 16:36  #463 
Sep 2008
Kansas
7066_{8} Posts 
Oh no! I've got i and n reversed in my above posts. I'll try to keep them straight going forward.
Table n=19 has been initialized to i=96 but there is still work to do. Many small remaining composites which I compete with the elves. Don't want to duplicate work. I'll let you know when I get it to a somewhat stable state. BTW, all the i=odd sequences terminate or mostly will terminate. But you already knew that. In the meantime I can start building Table n=23 next. Well, I mean initialize in FDB... 
20200820, 18:05  #464 
"Garambois JeanLuc"
Oct 2011
France
2·463 Posts 

20200820, 18:30  #465  
Aug 2020
23_{8} Posts 
Quote:
Quote:
For example, from conjecture 2), normally 5 is what provide a factor of 3 for s(n). But when k=5 (3^20) and we get a factor 5^2, we also get factor of 11 and 41, both of which also provide a factor of 3 for s(n). In this case I think conjecture 2) is true, but I can't prove it. P.S. Using LTE we find that 157^2 will divide s(3^(78*k)) if and only if 157 divide k (though we maybe have more than 157^2). 

20200820, 18:56  #466  
Aug 2020
19 Posts 
From post #364
Quote:
Since (p^{i}1) is a factor of (p^{(i*n)}1), s(p^{i}) is a factor of s(p^{(i*n)}) for all positive integer n. for odd a in general, this is not true. For example Code:
s(15^{(3)}) = 3 · 5 · 191 s(15^{(3*2)}) = 2 · 7 · 751 · 947 s(15^{(3*3)}) = 3 · 76091 · 147353 

20200820, 18:57  #467 
Sep 2008
Kansas
2·17·107 Posts 
Table n=23 has been initialized to i=88. Tables 19 & 23 can be instead in the web page with the understanding there is going to be many moving targets. FDB workers will factor small composites and I will slowly tackle the larger ones (up to C120).
In summary: Table n=18  all i <=77 terminate. Eventually all cells will most likely be green. Table n=19  It appears all i=odd sequences has or will terminate. Table n=23  It appears all i=odd sequences has or will terminate. Last fiddled with by RichD on 20200820 at 18:58 Reason: can't spell "initialized" 
20200820, 19:17  #468  
Oct 2006
Berlin, Germany
7^{2}·13 Posts 
Quote:
I now go up to 3^335. Nothing in base 6 was reserved. So I took all ub to 6^206. Last fiddled with by yoyo on 20200820 at 19:43 

20200821, 05:44  #469 
Oct 2006
Berlin, Germany
637_{10} Posts 
I take also up to 7^189.

20200821, 13:31  #470 
"Garambois JeanLuc"
Oct 2011
France
2·463 Posts 
OK, page updated.
Thank you all very much for your work ! Thank you for pointing out possible handling errors. Base 18 added. Base 19 added. Base 23 added. Bases 3, 5, 6, 7, 10, 11, 12, 13, 14, 15 and 17 have been extended. @RichD : Can you please confirm that the attributions are good for green cells ? All cells in base 18 are green, because if n=18^i, s(n) becomes odd for all i. Indeed, n here is always even and we know that there is a change of parity if n is a perfect square or twice a perfect square. If i is even, then n is a perfect square, this is obvious. If i is odd, we pose i=2*k+1 and thus 18^(2*k+1)=(2*3^2)^(2*k+1)=2^(2*k+1)*3^(2*(2*k+1))=2*2^(2*k)*3^(2*(2*k+1)) which is thus a double of a perfect square. Thus, for the bases 18=2*3^2, 50=2*5^2, 72=2*6^6, 96=2*7^2... all squares will be green ! Last fiddled with by garambois on 20200821 at 13:55 Reason: To give more information about the changes to the page... 
20200821, 13:47  #471  
"Garambois JeanLuc"
Oct 2011
France
1110011110_{2} Posts 
Quote:
I'm beginning to understand the mechanism, thanks again to you for your explanations ! Your reasoning seems to be able to establish what we can guess with our calculations. Seeing this, I tell myself that it is no longer worth continuing to formulate such conjectures, like those of post #447. Therefore, we can focus on other phenomena. But, do you also think that it is no longer worthwhile to formulate conjectures like those of post #447, or do you think that this kind of conjecture can still be of interest ? On the other hand, don't hesitate to let us know if you have an idea to test based on our data that you might have had ! 

20200821, 13:49  #472 
"Garambois JeanLuc"
Oct 2011
France
2·463 Posts 

20200821, 14:00  #473  
Sep 2008
Kansas
E36_{16} Posts 
Quote:
On the other hand, if a sequence starts say above C75, then I need to run the calculations to get it down to where the workers can finish it off. That being said, for Table n=18, "A" should be added to "i=" 610, 12,14, 16, 1822, 2426, 3031, 33, 36, 38, 40, 4243, 49, 57. Likewise for n=19 and n=23. 

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