A generalization of the Collatz problem and conjecture

TL;DR

This paper introduces a broad class of integer mappings extending the Collatz problem and conjectures that many of these mappings also always reach unity regardless of the starting number.

Contribution

It generalizes the Collatz problem by defining an infinite set of mappings and hypothesizes that many share the same convergence property.

Findings

Proposes an infinite set of generalized Collatz mappings

Conjectures that many mappings in this set converge to unity

Extends the scope of the original Collatz conjecture

Abstract

We introduce an infinite set of integer mappings that generalize the well-known Collatz-Ulam mapping and we conjecture that an infinite subset of these mappings feature the remarkable property of the Collatz conjecture, namely that they converge to unity irrespective of which positive integer is chosen initially.