The distribution of self-numbers in arithmetic progressions (Q1331771)

Let \(f(a)\) denote the sum of the digits of the integer \(a\) in a given scale. A self-number is an integer \(n\) for which the equation \(n= a+f(a)\) has no solutions. In this paper the results of \textit{U. Zannier} [Proc. Am. Math. Soc. 85, 10-14 (1982; Zbl 0498.10008)] on the counting function for the set of self-numbers are extended to arithmetic progressions.