Checking Collatz Conjecture
Here’s an example of the iteration process starting with the number 6:
f(6) = 6/2 = 3
f(3) = 9 + 1 = 10
f(10) = 10/2 = 5
f(5) = 3 × 5 + 1 = 16
f(16) = 16/2 = 8
f(8) = 8/2 = 4
f(4) = 4/2 = 2
f(2) = 2/2 = 1
The sequence generated by the iterative application of the Collatz function is often represented as a directed graph, with each number in the sequence represented by a node, and edges connecting nodes to their Collatz function outputs.
The sequence generated by the example above can be represented by the following graph:
6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1
Note: Collatz conjecture has been verified for all numbers up to 2.95×1020.
Collatz Conjecture: Fun Facts and More
Collatz Conjecture or 3n + 1 Conjecture or Ulam Conjecture, is the problem in mathematics for almost a decade. It is proposed in 1937 by Lothar Collatz. Although extensively tested and always found true, this conjecture remains unproven, making it a persistent and enticing mystery in the world of mathematics.
Famous mathematicians Paul Erdős said about the Collatz Conjecture, “Mathematics may not be ready for such problems,” highlighting its deceptive simplicity and deep complexity. In this article, we will discuss this conjecture which seems true but still not proven by scholars.
Table of Content
- What is Collatz Conjecture?
- Notation of Collatz Conjecture
- Other Names for Collatz Conjecture
- Checking Collatz Conjecture
- Examples of Collatz Conjecture
- Fun Facts about the Collatz Conjecture
- FAQs: Collatz Conjecture