Geodesic
Small Digitwise perturbations of a~number make it normal to unrelated bases
Lobachevskii journal of mathematics, Tome 11 (2002), pp. 22-25

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Let $r,g\ge 2$ 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. 
@article{LJM_2002_11_a4,
     author = {L. N. Pushkin},
     title = {Small {Digitwise} perturbations of a~number make it normal to unrelated bases},
     journal = {Lobachevskii journal of mathematics},
     pages = {22--25},
     publisher = {mathdoc},
     volume = {11},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2002_11_a4/}
}
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L. N. Pushkin. Small Digitwise perturbations of a~number make it normal to unrelated bases. Lobachevskii journal of mathematics, Tome 11 (2002), pp. 22-25. http://geodesic.mathdoc.fr/item/LJM_2002_11_a4/