Experimental Observations on a Discrete Function Related to Odd Composite Numbers

This work presents a discrete function defined via an integer-part sum and a limit depending on the parameter . The analysis is primarily experimental and originates from the observation of a possible correlation between the growth of the function and the occurrence of odd composite numbers. In particular, a discrete difference of the form is examined, which appears to remain zero for many odd prime values, without constituting a proven primality criterion. No claim of a definitive discovery or universal validity is made in this work. The purpose is solely to document an empirical observation and to provide a reproducible framework for further investigation. The author acknowledges that the proposed construction requires deeper theoretical analysis and intends to further explore the topic in future work, should stronger mathematical evidence emerge.