This work presents an original conjectural study on the behavior of integer sequences generated by iterative mappings related to the classical � problem. By analyzing the evolution of integers through parity-dependent transformations, the work identifies structural patterns in last-digit behavior and residue classes. The conjecture proposes a systematic reduction mechanism that suggests convergence properties for broad classes of integers. While no complete proof is claimed, the observations are supported by logical deductions and heuristic reasoning. This manuscript is intended as a preliminary contribution, inviting further formal analysis and verification within number theory and discrete dynamical systems.
Krishna Chaudhry (2026) studied this question.