## Abstract

Applying the theory of distribution functions of sequences we find the relative densities of the first digits also for sequences *x _{n}* not satisfying Benford’s law. Especially for sequence

*x*=

_{n}*n*,

^{r}*n*= 1, 2, . . . and

*n*= 1, 2, . . ., where

*p*is the increasing sequence of all primes and

_{n}*r*> 0 is an arbitrary real. We also add rate of convergence to such densities.