# Tag Info

Dynamics of the iterated map $n \to 3n+1$ if $n$ is odd and $n \to \frac n2$ if $n$ is even. Generalizations to $n \to 3n-1$ or $n \to 5n+1$ or even to $n \to pn+q$ . Other names are "$3x+1$-problem","syracuse problem". If you have a question, please be specific to your detail. MSE is not intended to check attempted proofs.
The Collatz Conjecture asserts that every positive integer, when iterated under a function taking odd $n$ to $3n+1$ and even $n$ to $\frac{n}2$, will eventually be transformed to $1$.
The questions around the conjecture are questions about the status of the $3n+1$ problem or that of its generalizations and about literature. Since it is an exponential diophantine problem which is iterated according to residues $\pmod 2$, such questions often deal with modular arithmetic and subsequent problems.
Also the general problem of approximation of powers of 2 to that of powers of 3 (in the original $3n+1$-formulation) occurs as determining ingredient.