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Old 2011-09-24, 13:17   #16
Mini-Geek
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"Tim Sorbera"
Aug 2006
San Antonio, TX USA

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Quote:
Originally Posted by schickel View Post
How about we delete the ones that manage to escape from the top post and move the sequence to the main reservation thread, unless indicated otherwise by the escapee?
It'd be more work, and considering the 3 can come and go pretty easily, I don't really want to do it this way. I, for example, plan to run 199710 until it settles into a driver (currently driverless with 2^5*7^2*11) or grows too large for me to handle. I'd expect many others would do similar. I'd prefer to leave it in this thread until they say otherwise. (it's not like it prevents this subproject from being complete - we can mark sequences that are no longer 2^2*3 if that'd make things clearer)
Quote:
Originally Posted by schickel View Post
So does the exponent on the 3 matter? Also, does this change the sequences that get posted for work on this project? (Actually, at the very least, it lets out sequences with 5 raised to an odd power, correct? That takes 71 more out of play right off the bat....)
AFAICT, no, the exponent on the 3 doesn't matter, because sigma(3^n) mod 3 is 1 for any n>=0. If you want to hit the most likely to break first, yes, you'd avoid sequences with 5 raised to an odd power, (because they can't lose it on the very next line) but depending on how hard it is to lose that 5 or change its power, it might be a very minor difference.
A little more on my methods and why "sigma(3^n) mod 3 is 1" is important: see the formula for calculating the sigma of a number. If the current line is divisible by 3, that means it is 0 mod 3. Once we have its sigma, the next line is sigma - lastLine. Working mod 3, that's sigma - 0, or sigma. So for the next line to not be divisible by 3, sigma != 0 mod 3 must be true. The sigma is the product of a series of numbers, which are the sigmas of the prime factors, e.g. sigma(2^2*3)=sigma(2^2)*sigma(3). If none of these numbers multiplied together are 0 mod 3, (i.e. all are -1 and 1, or 1 and 2 if you prefer) then the sigma will not be 0 mod 3, and so the next line will not be 0 mod 3.
I'm sure I'm stating trivialities for mathematicians, but considering I'm the first in this thread to mention how to lose the 3, it might be of some use for learning for everyone.

Last fiddled with by Mini-Geek on 2011-09-24 at 13:26
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