Successive Occurrence of a Non-Zero Digit in
All Base b Natural Numbers Less Than b
n

Neeraj Anant Pande

doi:https://doi.org/10.14445/22315373/IJMTT-V39P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 39 | Number 1 | Year 2016 | Article Id. IJMTT-V39P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V39P505

Successive Occurrence of a Non-Zero Digit in All Base b Natural Numbers Less Than b n

Neeraj Anant Pande

Abstract

Considering base b number system for any positive integer b > 1, all successive positive integers less than bn , for any positive integer n, are under consideration. Successive occurrences of digit 1 in initial numbers less than bn in base b are analyzed here. The formulae for the number of occurrences of successive 1’s, first and last instance in base power ranges are developed. This is done for all occurrences of multiple number of successive 1’s and finally all results are generalized for such successive occurrences of all non-zero digits. Tabulated values are provided for computer friendly base b = 16.

Keywords

General base, Natural numbers, non-zero digit, successive occurrences.

References

[1] Neeraj Anant Pande, “Numeral Systems of Great Ancient Human Civilizations”, Journal of Science and Arts, Year 10, No. 2 (13), (2010), pp. 209-222.
[2] Neeraj Anant Pande, “Analysis of Occurrence of Digit 1 in Natural Numbers Less Than 10n”, Advances in Theoretical and Applied Mathematics, 11(2), (2016), pp. 99-104.
[3] Neeraj Anant Pande, “Analysis of Successive Occurrence of Digit 1 in Natural Numbers Less Than 10n”, American International Journal of Research in Science, Technology, Engineering and Mathematics, 16(1), (2016), pp. 37-41.
[4] Neeraj Anant Pande, “Analysis of Non-successive Occurrence of Digit 1 in Natural Numbers Less Than 10n”, International Journal of Advances in Mathematics and Statistics, Accepted, (2016).
[5] Neeraj Anant Pande, “Analysis of Occurrence of Digit 0 in Natural Numbers Less Than 10n”, American International Journal of Research in Formal, Applied and Natural Sciences, Communicated, (2016).
[6] Neeraj Anant Pande, “Analysis of Successive Occurrence of Digit 0 in Natural Numbers Less Than 10n”, IOSR-Journal of Mathematics, Vol.12, Issue 5, Ver. VIII, (2016), pp 70 – 74.
[7] Neeraj Anant Pande, “Analysis of Non-successive Occurrence of Digit 0 in Natural Numbers Less Than 10n”, International Journal of Emerging Technologies in Computational and Applied Sciences, Communicated, (2016).
[8] Neeraj Anant Pande, “Analysis of Occurrence of a Non-Zero Digit in All Base b Natural Numbers Less Than bn”, International Journal of Computational Science and Mathematics, Communicated, (2016).
[9] Nishit K. Sinha, “Demystifying Number System”, Pearson Education, New Delhi, 2010.

Citation :

Neeraj Anant Pande, "Successive Occurrence of a Non-Zero Digit in All Base b Natural Numbers Less Than b n," International Journal of Mathematics Trends and Technology (IJMTT), vol. 39, no. 1, pp. 29-33, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V39P505