Dynamics of the Digit Sum of Integer Powers: Cycle Structure and Finite Search
Year: 2026
Type: preprint
Abstract: Superseded by Version 3 English version of the Portuguese preprint previously deposited in Zenodo as “Dinâmica da Soma dos Algarismos de Potências: Ciclos e Busca Finita”. This manuscript studies the iterative dynamics of the arithmetic function f_k(n) = s(n^k), where s(·) denotes the sum of digits in base 10 and k ≥ 2. The paper proves an explicit finite bound for the location of cycles, reducing the cycle search to a finite problem, and reports exact computational classifications for 2 ≤ k ≤ 10. This version updates the manuscript language to English and includes revised figures prepared for arXiv submission.
Institution: Agência Nacional de Energia Elétrica
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140753958
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