Distribution of Leading Digits of Numbers

Yukio Ohkubo; Oto Strauch

doi:10.1515/udt-2016-0003

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Distribution of Leading Digits of Numbers

Uniform distribution theory

Volume 11 (2016): Issue 1 (June 2016)

By: Yukio Ohkubo and Oto Strauch

Open Access

|Jan 2017

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.

References

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Articles in this issue

DOI: https://doi.org/10.1515/udt-2016-0003 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 23 - 45

Submitted on: Sep 23, 2015

Accepted on: Nov 14, 2015

Published on: Jan 13, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Benford’s law,

distribution function,

prime number

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2017 Yukio Ohkubo, Oto Strauch, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 11 (2016): Issue 1 (June 2016)