Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Uniform distribution theory

The Journal of Slovak Academy of Sciences

1 Issue per year


Mathematical Citation Quotient (MCQ) 2016: 0.40


Emerging Science

Open Access
Online
ISSN
2309-5377
See all formats and pricing
More options …

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

Jean-Marc Deshouillers
  • Université de Bordeaux, Bordeaux INP et CNRS, Institut mathématique de Bordeaux, UMR 5465, 33405 TALENCE Cedex, France
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-01-13 | DOI: https://doi.org/10.1515/udt-2016-0018

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.

Keywords: radix representation; automatic sequences; significant digit; factorial; base 12

MSC 2010: 11A63; 11B85

REFERENCES

  • [1] ALLOUCHE, J-P.—SHALLIT, J.: Automatic Sequences, Cambridge University Press, Cambridge, UK, 2003.Google Scholar

  • [2] COBHAM, A.: Uniform tag sequences, Math. Systems Theory 6 (1972), 164–192.Google Scholar

  • [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.Google Scholar

  • 4] DESHOUILLERS, J-M.: A footnote to The least non zero digit of n! in base 12, Uniform Distribution Theory 7 (2012), 71–73.Google Scholar

  • [5] DESHOUILLERS, J-M.—RUZSA, I.: The least non zero digit of n! in base 12, Pub. Math. Debrecen 79 (2011), 395–400.Google Scholar

  • [6] DRESDEN, G.: Three transcendental numbers from the last non-zero digits of nn, Fn and n!, Math. Mag. 81 (2008), 96–105.Google Scholar

  • [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.Google Scholar

  • [8] SLOANE, N. J. A.: The On-Line Encyclopedia of Integer Sequences, http://oeis.org; key word: Final nonzero digit of n!Google Scholar

  • [9] STEWART, C. L.: On the representation of an integer in two different bases, J. Reine Angew. Math. 319 (1980), 63–72.Google Scholar

About the article

Received: 2016-03-26

Accepted: 2016-10-13

Published Online: 2017-01-13

Published in Print: 2016-12-01


Citation Information: Uniform distribution theory, Volume 11, Issue 2, Pages 163–167, ISSN (Online) 2309-5377, DOI: https://doi.org/10.1515/udt-2016-0018.

Export Citation

© 2016 Jean-Marc Deshouillers, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in