On the Greedy Expansion of Egyptian Fractions for Composite Denominators of the Form $(6x-1)(6y-1)$

This paper analyzes the behavior of the greedy algorithm for the expansion of unit fractions of the form $\frac{3}{k}$, where the denominator $k$ belongs to the infinite family of composite numbers generated by the product of the form $(6x-1)(6y-1)$. The inefficiency of such an expansion is examined in comparison with shorter-length representations, linking the results to the OEIS A395997 sequence proposed by the author.