For example, 7x3=21, 5x9=45, etc. If you do, what is it?
–
We ask your questions so you don’t have to! Submit your questions to have them posted anonymously as polls.
YES YES YES
3x+1 Problem
or the Collatz conjecture
I love graphing random numbers and just seeing it go “Weee!— woahhh AHHHHHH!!”
I spent a semester deepdive studying the patterns in the Collatz Conjecture and genuinely started going insane.
I had to stop all my research for two weeks because I could genuinely feel myself losing my grip on reality.
Well it’s infamous for a reason
Here’s the insane thing I discovered: Someone proposed an alternate and equivalent problem called the reduced Collatz Conjecture. The only difference from the regular Collatz is that it says we can do the Collatz transformations and will eventually get a number less than what we started with rather than getting to 1. Functionally, we’re just doing the Collatz transformations like normal, but just stopping early.
And what I found when looking into this approach is that EVERY positive integer can be classified into a set of numbers such that every number in that set are all equivalent under the modulo of some specific power of 2 and every integer in each set goes through the EXACT same series of transformations to get to a number less than themselves.
Also, the number of odd transformations and even transformations depends on which power of two the set is based on but different sets grouped by the same power of two have different permutations of the transformations.
And the final thing I found that really made me spiral into insanity is the ratio of the starting number vs the first number less than what we start with trends toward a constant value as our starting number approaches infinity. But each set has a different ratio number.