We study the relationship between the frequency of a ternary digit in a number and the asymptotic mean value of the digits. The conditions for the existence of the asymptotic mean of digits in a ternary number are established. We indicate an infinite everywhere dense set of numbers without frequency of digits but with the asymptotic mean of the digits.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 3, pp. 302–310, March, 2014.
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Klymchuk, S.O., Makarchuk, O.P. & Prats’ovytyi, M.V. Frequency of a Digit in the Representation of a Number and the Asymptotic Mean Value of the Digits. Ukr Math J 66, 336–346 (2014). https://doi.org/10.1007/s11253-014-0934-7
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DOI: https://doi.org/10.1007/s11253-014-0934-7