In this paper sequences of integer numbers are defined and their properties are examined. The equivalent of Kurepa's hypothesis for the left factorial is given using the sequence $\{dn\}$. It is shown that the sequence $\{dn\}$ the base of papers of [5](G. V. Milovanović) and [8], [9] (Z. Sami). In view of the generalization of Wilson's theorem given in [1] (V. Kirin) it is shown that some results of papers [8] and [9] can be obtained by elementary methods. The prablem which is more general then the problem of Kurepa's hypothesis is considered.