Originally Posted by
Vyger
Lets start with the basics; I've been working on a problem in Number Theory off and on for almost ten years called "the Collatz Conjecture" aka "the 3X + 1 problem". Let f(x) be a function defined on the positive integers such that:
f(x) = x/2 if x is even
f(x) = (3*x+1)/2 if x is odd
Then the conjecture is: iterates of f(x) will eventually reach 1 for any
initial value of x. Is this right? Let me know what you think, I'm sort of stumped.
Ahh yes, HOTPO. I think it's ok to be stumped Vyger.
The Collatz conjecture is an unsolved conjecture in mathematics. If memory serves, it is named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, as the Ulam conjecture (after Stanislaw Ulam), or as the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers, or as wondrous numbers.
They take any whole number n greater than 0. If n is even, they halve it (n/2), else they do "triple plus one" and get 3n+1. The conjecture is that for all numbers this process converges to 1. Hence it has been called "Half Or Triple Plus One", sometimes called HOTPO.
Paul Erdős said about the Collatz conjecture: "Mathematics is not yet ready for such confusing, troubling, and hard problems."
In 2006, researchers Kurtz and Simon, building on earlier work by J.H. Conway in the 1970s, wrote that a natural generalization of the Collatz problem is recursively undecidable.
But, feel free to keep working on it if you would like...
