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Distribution of Leading Digits of Numbers Cover

Distribution of Leading Digits of Numbers

By: Yukio Ohkubo and  Oto Strauch  
Open Access
|Jan 2017

References

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  2. [2] BALÁŽ, V.—NAGASAKA, K.—STRAUCH, O.: Benford’s law and distribution functions of sequences in (0, 1) (Russian), Mat. Zametki 88 (2010), no. 4, 485–501; (English translation) Math. Notes 88 (2010), no. 4, 449–463.
  3. [3] BENFORD, F.: The law of anomalous numbers, Proc. Amer. Phil. Soc. 78 (1938), 551–572 (Zbl 18, 265; JFM 64.0555.03).
  4. [4] DIACONIS, P.: The distribution of leading digits and uniform distribution mod 1, The Annals of Probability 5 (1977), no. 1, 72–81.10.1214/aop/1176995891
  5. [5] ELIAHOU, S.—MASSÉ, B.—SCHNEIDER, D.: On the Mantisa distribution of powers of natural and prime numbers, Acta Math. Hungar. 139 (2013), no. 1–2, 49–63.
  6. [6] NEWCOMB, S.: Note on the frequency of use of the different digits in natural numbers, Amer. J. Math. 4 (1881), 39–41 (JFM 13.0161.01).10.2307/2369148
  7. [7] OHKUBO, Y.: On sequences involving primes, Uniform Distribution Theory, Vol. 6 (2011), no. 2, 221–238.
  8. [8] ROSSER, J. B.—SCHOENFELD, L.: Approximate formulas for some functions of prime numbers, Illinois. J. Math. 6 (1962), 64–94.10.1215/ijm/1255631807
  9. [9] STRAUCH, O.—BLAŽEKOVÁ, O.: Distribution of the sequence pn/n mod 1, Uniform Distribution Theory 1 (2006), no. 1, 45-63.
  10. [10] STRAUCH, O.—PORUBSKÝ, Š.: Distribution of Sequences: A Sampler, Peter Lang, Frankfurt am Main, 2005.
DOI: https://doi.org/10.1515/udt-2016-0003 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 23 - 45
Submitted on: Sep 23, 2015
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Accepted on: Nov 14, 2015
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Published on: Jan 13, 2017
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 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.