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 …

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 …

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The Collatz Conjecture is a famous conjecture in mathematics that has lasted for over 70 years. It goes as follows: Define $f(n)$ to be as a function on the natural ...

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. …

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 …

Jun 28, 2021 · An analogue to the Collatz conjecture with these rules fails, because $\ 5\to 14\to 7\to 20\to 10\to\ 5\ $ is a cycle that does not contain $\ 1.\ $ In fact, there are lots of cycles that …

Nov 14, 2021 · I think it makes sense to consider every case of the generalized version of the Collatz-conjecture to be a Collatz-like problem. Note that this generalized version was proven …

I suppose if the Collatz Conjecture proves to be true, that is each sequence will terminate in a 4-2-1 loop, then there will always be a prime number in any Collatz sequence.