Distribution of Leading Digits of Numbers

Ohkubo, Yukio; Strauch, Oto

doi:10.1515/udt-2016-0003

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 $x_{n} = p_{n}^{r}$ $x_n = p_n^r $, n = 1, 2, . . ., where p_n is the increasing sequence of all primes and r > 0 is an arbitrary real. We also add rate of convergence to such densities.

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Distribution of Leading Digits of Numbers

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