/sci/ - Science & Math

>anon literally wants to prove Collatz by naive exhaustion
I am amazingly angry.

>>11299259
This method is better at testing numbers to show just how large a number needs to be to disprove the conjecture. Obviously we can’t exhaust all numbers, we’d have to prove that mathematically, but there’s a chance that the program would stop at some special number and indicate a number that does disprove the conjecture

>>11299259
>>11299287
I realize that if the program were allowed to run a long time, then it wouldn’t prove or disprove anything. But it would show us the possible forms of numbers that never reach below themselves, and if these numbers can indicate how large the first number must be. The process can also point out cycles if we program it to. So there’s a possibility that we find forms that do not get eliminated by the process, indicating that they represent a possible counterexample

>>11299252
The Collatz conjecture has been tested for all numbers up to 10^20, and you are not going to get that far using this method (you might get to 10^12-13).

You can still try for fun, though.

>>11299362
why wouldn’t this method be better? You’re eliminating so many possible numbers. Even if you’re not checking the forms themselves, you could use evaluate the numbers while using a few form specifications to skip numbers that you know aren’t disproving the conjecture. We can skip all evens, all numbers of the form 4n + 1, etc.

anon wtf did you use that OP pic

>>11299386
Because 10^20 is a lot, try summing 1 to a double variable in a while loop using C and see how far you get.

>>11299394
nghh....

>>11299401
but my method isn’t going through each number like that. I’m generating candidate forms such as 16n + 7/9/15 which shows that 7 is the minimum number for candidacy. As the process continues, this number gets larger, eliminating more and more numbers. Or we can use the normal method of checking every number and seeing if it goes to 1 (or below itself), but first skipping numbers matching the forms that we’ve already eliminated.

>>11299417
The point is that the number of operations a processor can do in a second is not a lot compared to 10^20.

How far do you expect your sieve algorithm to grow? Can you estimate?

>>11299425
how fast*

>>11299425
It’s difficult to estimate because I haven’t run the process that much. The problem is that each candidate form generates its own list of candidate forms, so that the number of forms you have to check grows exponentially, but the point as that we should always be checking the smallest form (whichever has the smallest constant in its form). But I haven’t bothered to run through the 256n and 65,536n forms yet, and I don’t know how to program this, so I don’t know how fast it would take.

>>11299460
Ok I'm thinking about it.

>>11299460
Suppose you could enumerate a set of forms for which the Collatz conjecture is valid, all of which can be written as

a + b*n

then to test a given N you would have to iterate through all forms and check if that N can be written in that particular form by asking "is (N-a)/b = 0?", is that correct?

If so that is an O(N) algorithm, that requires a check for each natural, and is not fast

>>11299839
or you could just loop with a set of instructions, such as skip 8 numbers, then skip 5, then skip 3, repeat.

>>11299915
probably not good numbers for the example but consider our forms 16n + 7/11/15, then our loop has to include

7, 11, 15, 23, 27, 31, etc.

So we’re skipping three numbers twice, then 7, then repeat. With just a few more processes we can make our loop even more restrictive

>>11299352
i actually did work on that for a while and found that the numbers with longest relative time of fly where numbers of the form 2^n +/- 1 IIRC.
i don't even remember how i proved it but if i found it there must be a proof by someone else online

>>11300139
Yes I found that a while back too.

2^n - 1
3*2^n - 2
3*2^n-1 - 1
.
.
3^n - 1

So the larger the n, the longer this process.

bump

>>11299252
Hey OP, I have done quite an extensive amount of work on this take on the collatz conjecture. If you would like to talk we can discuss this on discord.

>>11300908
why not just post whatever you wanted to post here instead of selfishly trying to export the discussion, you dumb redditor?

>>11300945
Because it is a lot of information retard, I don't have the time to sit and type all of what I have found out on an anonymous board. I'd rather discuss this verbally. You are welcome to join.

>>11300955
You seem to misunderstand the concept of 4chan.
We don't export our discussion to other means of communication; we've pulled all the raids and meme campaigns and all that stuff, which were successful regardless if you agree with them or not, right here under the form of open discussion in the same manner that it was started: as a post on 4chan. You don't just use this website as your personal launchpad or billboard to then funnel certain posters into a new environment. This is not your quality poster recruitment bureau because what you're essentially trying to do is to take the OP away from 4chan and have him pollinate your discord, which is a selfish abuse of the board and his selfless desire to discuss or share insights without any identity attached to him.

>>11300964

>>11300964
Jesus Christ, I'll kindly take my leave. To have the nerve to claim that I'm trying to "pollinate my discord". I have no words.

>>11300968
oh no the selfish poster who contributed nothing to the thread is leaving how will we EVER cope with this bros

>>11300971
You can cope by trying to solve the Collatz conjecture, which will be a futile attempt no doubt. Good luck.

Have you seen this https://youtu.be/U7LrFp9RBek ?

>>11300964
This is the first erection worthy post I've seen. Glad to witness the 4chan gestalt come to its own awareness that those that post on 4chan conclude and resolve their shit on 4chan because who cares about going to some 'cozy quiet corner' just because someone felt awkward at the word orgy we engage in.

>>11300996
i dont get it
t. negative iq

>>11299417
Did you consider 16n + 3?

>>11301067
16n + 3 is derived from 4n + 3 only if our first n is divisible by 4 (4n). But this fails as it leads to all numbers of this form going below itself in just a few steps >>11299252
Notice how I used 4n + 1/2/3 as substitutes but not 4n. Now sometimes it might be the case that you can substitute xn which wouldn’t affect the added constant, but if we could prove mathematically that the form could not stay constant, then we would essentially be proving that there is no collatz number, since there would be no possible form for it. Any candidate form needs to be further “specified,” so that the process goes to infinity and all numbers are eventually eliminated

>>11301053
We try to bring order into the chaos. To do that the idea is to take a function f(x) and apply it to itself like f(x), f(f(x)),... continously (simple recursion).
Example: f(x)=3x+1 gives the sequence 4,13,40,... when x = 1.
Now we say that the value that we've first insterted into the recursion (1 in our example) is the y coordinate in a 2d coordinate system and the x coordinate is the result. Point p1=(f(x),x) , p2=(f(f(x)),x), ... we can enumerate the recursive depth and write it down: p1(depth)=(f(f(f...(dependent on depth(x)))...),x)
We then use the next odd number that hasn't appeared as a result yet, which is 3 (we've only used 4,13,40,... etc) and then insert 3 in our function and we get 3,10,31,... so we draw these points in our system p(depth 0)=(3,3), p(d 1)=(10,3)...

We do the exact same shit with 2x+1. Then we negate the y value of the 3x+1 function and draw arrows between the same numbers of the 2x+1 and 3x+1 functions. Then we draw points and shift these along the arrows.

>>11301099
I forgot to mention: There always exists a distance vector between 2 results of a function: d=f(x+1)-f(x) and you can imagine numbers of a function as balls traveling along this vector instead of frogs jumping from one result to another

>>11301091
or if we could prove that a form could keep its constant, for example let’s say 16n + 11 could lead to 256n + 11, then to 65,536 + 11 and so on, preserving the 11. If this 11 is certain to never be eliminated, then wouldn’t it mean that 11 itself is a collatz number? Obviously I’m just using 11 as an example.

I haven’t really done much math on this trying to prove that you can/cannot always just substitute back in some xn an preserve the constant forever, but it seems like this proof could solve everything

>>11300908
I don’t see how talking is more efficient. Just post pics of your work with small comments

>>11300974
Just fuck off already, you soggy vagina.

More process. This would be pretty difficult to program as now there are 19 forms. I guess I could create a large array to store all these pairs of numbers into each row, and modifying as the process keeps going. I’d simply have to loop through the array to find my lowest constant and perform the process on that form, then eliminate it and add the new forms, and repeat.

>>11301215
not sure how I dropped my 2^n - 1 cases

>>11301215
what are these supposed to represent?

>>11301297
Apologies, sets of possible candidates that disprove the conjecture

>>11301299
How old are you? 5?

>>11301327
now you’re just outing yourself as underage

>>11299252
Don't know if related. But these guys: mathoverflow.net/questions/348733/arithmetic-progressions-in-stopping-time-of-collatz-sequences suggest that starting numbers [math](2^a3^b)^n+1[/math] are particularly interesting.

>>11301426
>>11301451
Looking for patterns in the conjecture is useless, there are infinitly many of them. You're just wasting your time.

Related: https://www.youtube.com/watch?v=BNOQUPmgbnY

>>11301481
prove it

>>11301215
I’m gonna write a simple program to do all these calculations for me so I can figure out which numbers to test as I said here >>11300065
I might be able to test a small percentage of numbers, allowing me to simply test every number beyond what’s known as the largest numbers that uphold the conjecture, for fun