Posts by Seth Hill
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1) Message boards : Science : The Collatz Conjecture (Message 5406)
Posted 2933 days ago by Seth Hill
Do you know which number has the highest ratio of 3x+1 operations to /2 operations in its sequence? Well, it's not a very large number, it's 993. So in some sense, 993 was the closest candidate so far ;)


Looks like there are 61 divisions and 93 steps, so the ratio's about 0.52?

The strong law of small numbers strikes again (I guess?!). Collatz seems to provide endless opportunities for little oddities like this.
2) Message boards : Science : The Collatz Conjecture (Message 5401)
Posted 2933 days ago by Seth Hill
Has some other research project already calculated the numbers up to 10e291 or created some type of proof that no numbers less than 10e291 could have an infinite number of steps?


I assume not. As far as a proof, my own attempts at a proof have so far been unsuccessful. If that changes I'll let you know :P

I mainly was trying to figure out what exactly the project was calculating. My examples were trying to point out that you can count steps really fast. When I first found the project, I had the impression that you were just trying to find numbers that had the most steps to 1.


The beauty of the applications we are using is that they are fast (600 MILLION numbers calculated per second).


Do you take into account previously checked numbers? Meaning that, for example, if you come across 2^n, does the algorithm know enough to stop there and return n?


(BTW, you chose even numbers for your example. You could have chosen two numbers half their size as the first step would be to divide by 2.)


Ah, so I did. As I said, I just mashed my number keys long enough to get a couple sufficiently large examples ... 50% chance of even numbers!
3) Message boards : Science : The Collatz Conjecture (Message 5355)
Posted 2934 days ago by Seth Hill
I'm just curious how this project can prove Collatz Conjecture


I'm pretty curious about that too. More than that, I'm also curious why the numbers being computed are so small. What's the highest number that you've reached?

Your best results example is 2,362,032,211,856,451,015,323 with 2514 steps to one, is on the order of 10e21.

Here are a couple examples chosen by keyboard mashing, and calculated in well under a second on my 3 year old laptop:

38407962098672039845720938456023984650923847502398750329847502398475029348693847
57890243785789078092347890578324578023078457897839025478780234785879023487578234
78587032784870623806468238704567802348757823780458702 -> 5057 steps, on the order of 10e211

38407962098672039845720938456023984650923847502398750329847502398475029348693847
57890243785789078092347890578324578023078457897839025478780234785879023487578234
78587032784870623806468238704567802348757823780458702287034592836709875967438239
57462395871039456023984562809374509182374029763972388 -> 7887 steps, on the order of 10e291

Cheers,
Seth[/quote]




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