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.

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 …

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 …

Jan 24, 2022 · The Collatz conjecture has moreover a property that most conjectures like Goldbach or Riemann do not have. If there is a diverging trajectory , we might not be able to prove that within …

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 …

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 …

Sep 4, 2021 · I have written some code that searches for counter-examples to the Collatz conjecture. The following fact enables me to accelerate the search. In the paper "Garner, Lynn - On The …

Dec 27, 2024 · In the case of the Collatz Conjecture, which states that "If a term is even, the next term is one half of it. If a term is odd, the next term is $3$ times the previous term plus $1$. The conj...

Oct 20, 2024 · He used the Collatz –Wielandt formula described above to extend and clarify Frobenius's work. $^ { [29]}$ Another proof is based on the spectral theory $^ { [30]}$ from which part of the …