Frequency of a Digit in the Representation of a Number and the Asymptotic Mean Value of the Digits

S. O. Klymchuk; O. P. Makarchuk; M. V. Pratsiovytyi

doi:10.1007/s11253-014-0934-7

paper

Frequency of a Digit in the Representation of a Number and the Asymptotic Mean Value of the Digits

arXiv:2603.04877 · doi:10.1007/s11253-014-0934-7

Abstract

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.