Some thoughts on the Collatz Conjecture

Been reading about the Collatz Conjecture lately. Just wanted to share some observations. The Setup Start with any positive integer n: If n is even, divide by 2 If n is odd, multiply by 3 and add 1 Repeat The claim: you'll always eventually reach 1. I find it interesting that a middle schooler can understand the rules, yet nobody has proven it. Take 27: 27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → 214 → 107 → 322 → ... → 1 Takes 111 steps, peaks at 9232. What I've Read From what I understand: Checked computationally up to about 3 × 10²⁰ Terras (1976) showed "almost all" numbers work (in some precise sense) Tao (2019) strengthened this result But there's no proof for all numbers. What Seems Hard The operation mixes two different types of behavior: Division by 2 (predictable) 3n + 1 (less predictable) Erdős apparently said mathematics may not be ready for such problems. Not sure what to make of that, but it's interesting. Patterns I Noticed Looking at "stopping time" (steps until