How many steps to reach 1? (Collatz Conjecture)

4.7k Views Asked by At

Is there some sort of algorithmic process or equation to determine the number of steps required for any given integer n to reach 1 in the Collatz Conjecture without having to actually perform a massive amount of number crunching?

I'm talking about when you have to evaluate large numbers like $\\ 2.64 * 10^{3456}$

1

There are 1 best solutions below

1
On BEST ANSWER

I'm sure it's not the answer you're looking for, but the only algorithmic process known to work for all tested inputs is to repeatedly apply the Collatz function and count the number of applications required to reach 1. Even that is not proven for very large, untested numbers. That's what it means, that the conjecture is unsolved. If there were an equation for the number of steps then the conjecture might be solved by determining for which inputs the output is infinite.

If you look at Terrence Tao's blog I think he describes the rate at which inputs tend to converge on 1 among other things, but this is not proven for all inputs.