Aug 26, 2022 · Therefore the Collatz Conjecture is true. Every number will inevitably transform down to $1$. Sorry for the difficult to read LaTeX, kind of a new user, but feel free to criticize away about …

The Collatz conjecture is the simplest open problem in mathematics. You can explain it to all your non-mathematical friends, and even to small children who have just learned to divide by 2.

Mar 21, 2026 · You have shown that the minimum of a Collatz sequence that does not reach $1$ is odd. Since any even number gets divided by $2$, producing a smaller number, this is not hard.

Mar 10, 2026 · Q&A for people studying math at any level and professionals in related fields

Nov 3, 2024 · Here is a curiosity about negative Collatz sequences that it would be interesting to investigate: Do the -5 loop numbers ever become more frequent than the -1 loop and -17 loop …

Mar 31, 2018 · For all those infinite sequences the Collatz-conjecture is immediately proven - the Collatz-transformation (in its Syracuse-formulation) goes in reverse direction of the arrows, for …

Sep 25, 2015 · which extends the collatz function to the complex plane. I think the point to remember is that the way the Collatz function is written definitely influences how it's studied. This allows for new …

Aug 19, 2013 · I've just written a simple java program to print out the length of a Collatz sequence, and found something I find remarkable: Consecutive sequences of identical Collatz sequence lengths. …

6 I've been messing around with the Collatz sequences a bit, and have come across a few patterns - I was wondering if there are any known explanations for these patterns. The first is the plot of stopping …

Oct 20, 2024 · As per Wikipedia, it's been stated that Wielandt was able to prove Perron-Frobenius Theorem using Collatz-Wielandt Formula: A common thread in many proofs is the Brouwer fixed …