.comment-link {margin-left:.6em;}

Tuesday, March 22, 2005

 

22:20

So I got a call from my mom earlier and found out that my sister and cousins might be coming down with my uncle this evening. Later I got a call from my sister saying they weren't coming. I was doing homework in the quiet section of the library, so I turned off my phone after that. Later I went to work. After I got off work, I turned on my phone and there were three messages letting me know that: a) They were coming after all. b) They accidentally hit redial and recorded random noise on my voice mail. c) They were playing pool in the Student Union Building and I could join them after I got off work. So I did. That was fun. I didn't know my sister was that good at pool. They are driving home now.

There's a flier in the computer lab here advertising two math guest lectures on April 1st. One of them starts half an hour before I get off work, but I can make it to the second one. I'm very happy about this, because it's about Collatz' Conjecture. That's right, the open question in number theory that I've been mildly obsessed with since I was twelve. I'm almost excited about this.

Time to finish up Representation Theory homework.

Comments:
What (more/or/less) exactly is the Collatz Conjecture?
 
Pick a positive integer. If it is even, divide it by 2. If it is odd, multiply it by 3 and add 1. Rinse and repeat. The conjecture is that no matter what number you start with, you will eventually arrive at the number 1.

Examples:

3, 10, 5, 16, 8, 4, 2, 1

7, 22, 11, 34, 17, 52, 36, 13, 40, 20, 10...

9, 28, 14, 7...

15, 46, 23, 70, 35, 106, 53, 160, 80, 40...

19, 58, 29, 88, 44, 22...

21, 64, 32, 16...

25, 76, 38, 19...
 
ahh, very nifty.
 
I dare you to try 27.
 
27 > 82 > 41 > 124 > 62 > 31 > 94 > 47 > 142 > 71 > 214 > 107 > 322 > 161 > 484 > 242 > 121 > 364 > 182 > 91 > 274 > 137 > 412 > 206 > 103 > 310 > 155 > 466 > 233 > 700 > 350 > 175 > 526 > 263 > 790 > 395 > 1186 > 593

...
Ok,,,I gave up on the by-hand method and wrote a C++ program to deal with it...27 has 112 numbers (including the 27 and 1).
 
You see why I stopped at 25? *grins*
 
Yes, after the first ten numbers I did I figured you planned my pain lol. But the original number doesn't have to be odd right? (all the numbers you gave as examples were odd)
 
Yeah, but with an even number you immediately divide by 2, which gives you a smaller number that you've looked at already (if you are listing them in order).
 
Post a Comment



<< Home

This page is powered by Blogger. Isn't yours?