An approach to the transformation of periodic sequences

We consider a periodic sequence $\{c_k\}_{k=0}^\infty$ and investigate a numerical properties of an irrational number $\alpha = \sum_{k=0}^\infty \frac{c_k}{k!}$. As an application of our results we present a simple transformation of periodic sequence $\{c_k\}_{k=0}^\infty$ into aperiodic sequence.