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Old 2012-06-24, 23:34   #3
science_man_88
 
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"Forget I exist"
Jul 2009
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Quote:
Originally Posted by Dubslow View Post
So I'm sure we've all read Clifford's analysis page.

(Btw, I've created a mirror of that page and his "From the Trenches" page so that we don't have to deal with the archive, and so that someone could edit it should they feel so inclined. Of course, if Clifford makes his own comeback, I'll take these down.)

Anyways, the analysis classifies the drivers by their characteristics, by how "stable" they are.

Of course, that doesn't take into account other factors, like how much a driver increases a sequence, or how rare getting a 127^2 is. So, since I am not an expert (or even half-competent) in these matters, I'm asking: Is it possible to create an ordered list of drivers from "worst to first"? Obviously the downdriver would be "first". I imagine 2^2 would be next, followed by 2^3, since they tend to drop a sequence, albeit slowly (and they're not very stable).
Code:
Best
2
2^2
2^3
...
?
...
2^6 * 127 ??
Worst
(PS Are there any drivers which are missing from that table?)
Code:
for(a=1,60,for(b=1,#divisors(sigma(2^a)),if(sigma(divisors(sigma(2^a))[b])%(2^(a-1))==0,print(2"^"a"*"divisors(sigma(2^a))[b]))))
according to this code:

Quote:
2^1*1
2^1*3
2^2*7
2^3*3
2^3*15
2^4*31
2^5*21
2^6*127
2^9*1023
2^12*8191
2^16*131071
2^18*524287
2^30*2147483647
2^60*2305843009213693951
are all drivers but not all of the possible drivers, partly because I can't search higher how I have things set up. the bigger a driver is the rarer it likely is. as to biggest gains I would think the larger ones but all I know is possibly with numbers that are driver * prime.

Last fiddled with by science_man_88 on 2012-06-24 at 23:43
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