Progressive Cumulative Counting and Its Associated Integer Sequence

This document presents Version 2 (v2) of the Progressive Cumulative Counting procedure and its associated integer sequence. Version 2 corrects an error present in Version 1 regarding the transition rule after base-10 completion. The sequence is generated using two synchronized counting processes. The initial phase is based on direct natural counting. When the counting process reaches the completion of the elementary decimal base (digits 0–9), the system transitions to a cumulative rule where each new term is obtained by adding the current counting position to the previous result. The counting procedure and the resulting sequence can continue indefinitely, producing arbitrarily large integers. This document supersedes Version 1. Note: The core idea and underlying mechanism presented in this work were developed independently by the author. The mathematical formalization was refined with the support of assistive tools.