Has Collatz conjecture been proven?
Table of Contents
Has Collatz conjecture been proven?
The Collatz conjecture states that the orbit of every number under f eventually reaches 1. And while no one has proved the conjecture, it has been verified for every number less than 268. So if you’re looking for a counterexample, you can start around 300 quintillion. (You were warned!)
What is the length of the Collatz path for 5?
Collatz Problem
| # cycles | max. cycle length | |
|---|---|---|
| 3 | 17 | 118 |
| 4 | 19 | 118 |
| 5 | 21 | 165 |
| 6 | 23 | 433 |
What is Collatz sequence in Java?
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz. If n is even, the next number is n/2, if n is odd, the next number is 3n+1. The conjecture is that no matter what value of n, the sequence will always have as end values 4, 2, 1, 4, 2, 1, … .
What is the Collatz conjecture in Computer Science?
The Collatz conjecture equivalently states that this tag system, with an arbitrary finite string of a’s as the initial word, eventually halts (see Tag system#Example: Computation of Collatz sequences for a worked example).
What is the Collatz graph for positive integers?
The Collatz graph is a graph defined by the inverse relation So, instead of proving that all positive integers eventually lead to 1, we can try to prove that 1 leads backwards to all positive integers. For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 ≡ 4 (mod 6). Equivalently, n − 1
Are the first 21 levels of the Collatz graph generated bottom-up?
The first 21 levels of the Collatz graph generated in bottom-up fashion. The graph includes all numbers with an orbit length of 21 or less. There is another approach to prove the conjecture, which considers the bottom-up method of growing the so-called Collatz graph. The Collatz graph is a graph defined by the inverse relation
What is the longest sequence of consecutive numbers with identical Collatz lengths?
As it turns out, X = log (n) loglog (n) does the trick. TL;DR: between 1 and n, the longest sequence of consecutive numbers with identical Collatz lengths is on the order of log (n) loglog (n) numbers long.