Collatzlike
Collatzlike refers to a broad class of integer dynamical systems that generalize the structure of the Collatz (3n+1) problem. In its typical form, a Collatzlike map f operates on positive integers by applying a parity-dependent rule, most often f(n) = n/2 when n is even and f(n) = a n + b when n is odd, where a and b are fixed integers chosen to create a nontrivial, integer-valued trajectory. The original Collatz map corresponds to a = 3 and b = 1.
Variants expand or modify the rule. Some replace the odd-step with other linear forms, such as f(n)
Research questions focus on convergence, cycles, and stopping times. A central question is whether every starting
The term Collatzlike is used across number theory and dynamical systems to denote problems that resemble the