## L. Pushkin

## Small digitwise perturbations of a number
make it normal to unrelated bases

## (Lobachevskii Journal of Mathematics, Vol.11, pp.22-25)

Let $r, g\geq 2$ be integers such that $\log g/\log r$ is
irrational.
We show that under $r$-digitwise random perturbations of an expanded
to base~$r$ real number $x$, which are small enough to preserve $r$-digit
asymptotic frequency spectrum of $x$, the $g$-adic digits of $x$ tend to have the
most chaotic behaviour.

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