A Computational Exploration of Kaprekar's Routine: New Constants and Families in Bases 2–100

This preprint presents a computational exploration of Kaprekar's routine across bases 2–100 and digit lengths 2–10. Using a combination of Monte Carlo simulations and targeted exhaustive enumeration, the study identifies several previously undocumented Kaprekar constants, including a 4-digit constant in base 5, and reports empirical families of constants across multiple bases. The work further documents a deterministic family of 3-digit attractors in even bases, verified by exhaustive enumeration for all even bases up to 100, and proposes conjectures concerning 2-digit Mersenne bases and higher-dimensional Kaprekar dynamics. The paper also highlights regions of unusually complex behavior, particularly in base 4. All results are computationally reproducible, and the accompanying code and datasets are publicly available. The paper is intended as a contribution to experimental mathematics and as a foundation for future theoretical investigations of Kaprekar-type dynamical systems.