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

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).
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