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Višek [3] and Culpin [1] investigated infinite binary sequence $X=(X_1,X_2,\cdots )$ with $X_i$ taking values $0$ or $1$ at random. They investigated also real mappings $H\left(X\right)$ which have the uniform distribution on $[0;1]$ (notation $𝒰(0;1)$). The problem for $n$-ary sequences is dealt with in this paper.