Yet Another Footnote to the Least Non Zero Digit of n! in Base 12

Jean-Marc Deshouillers

doi:10.1515/udt-2016-0018

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Yet Another Footnote to the Least Non Zero Digit of n! in Base 12

Uniform distribution theory

Volume 11 (2016): Issue 2 (December 2016)

By: Jean-Marc Deshouillers

Open Access

|Jan 2017

Abstract

We continue the study, initiated with Imre Ruzsa, of the last non zero digit ℓ₁₂(n!) of n! in base 12, showing that for any a ∈ {3, 4, 6, 8, 9}, the set of those integers n for which ℓ₁₂(n!) = a is not 3-automatic.

References

[1] ALLOUCHE, J-P.—SHALLIT, J.: Automatic Sequences, Cambridge University Press, Cambridge, UK, 2003.10.1017/CBO9780511546563
Search in Google Scholar Back to article
[2] COBHAM, A.: Uniform tag sequences, Math. Systems Theory 6 (1972), 164–192.10.1007/BF01706087
Search in Google Scholar Back to article
[3] DEKKING, F. M.: Regularity and irregularity of sequences generated by automata. Seminar on Number Theory, 1979–1980 (French), Exp. No. 9, 10 pp., Univ. Bordeaux, Talence, 1980.
Search in Google Scholar Back to article
4] DESHOUILLERS, J-M.: A footnote to The least non zero digit of n! in base 12, Uniform Distribution Theory 7 (2012), 71–73.
Search in Google Scholar Back to article
[5] DESHOUILLERS, J-M.—RUZSA, I.: The least non zero digit of n! in base 12, Pub. Math. Debrecen 79 (2011), 395–400.10.5486/PMD.2011.5169
Search in Google Scholar Back to article
[6] DRESDEN, G.: Three transcendental numbers from the last non-zero digits of nⁿ, F_n and n!, Math. Mag. 81 (2008), 96–105.10.1080/0025570X.2008.11953536
Search in Google Scholar Back to article
[7] KAKUTANI, S.: Ergodic theory of shift transformations, in: Proc. The Fifth Berkeley Sympos. Math. Stat. and Probability (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, Part 2, Univ. of California Press, Berkeley, Calif., 1967, pp. 405–414.
Search in Google Scholar Back to article
[8] SLOANE, N. J. A.: The On-Line Encyclopedia of Integer Sequences, http://oeis.org; key word: Final nonzero digit of n!
Search in Google Scholar Back to article
[9] STEWART, C. L.: On the representation of an integer in two different bases, J. Reine Angew. Math. 319 (1980), 63–72.
Search in Google Scholar Back to article

DOI: https://doi.org/10.1515/udt-2016-0018 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 163 - 167

Submitted on: Mar 26, 2016

Accepted on: Oct 13, 2016

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:

radix representation,

Related subjects:

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2017 Jean-Marc Deshouillers, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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