On the distribution of self-numbers

Author:
U. Zannier

Journal:
Proc. Amer. Math. Soc. **85** (1982), 10-14

MSC:
Primary 10A30

DOI:
https://doi.org/10.1090/S0002-9939-1982-0647887-4

MathSciNet review:
647887

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Abstract: Self-numbers are those integers which cannot be expressed as , where denotes the sum of the digits of in a given scale. Here I prove that the number of self-numbers less than or equal to a large number equals , where is a strictly positive constant.

**[1]**M. Gardner,*Mathematical games*, Sci. Amer.**232**(1975), 113-114.**[2]**B. S. Recaman,*Solution to problem*E 2408, Amer. Math. Monthly**81**(1974), 407.**[3]**Kenneth B. Stolarsky,*The sum of a digitaddition series*, Proc. Amer. Math. Soc.**59**(1976), no. 1, 1–5. MR**0409340**, https://doi.org/10.1090/S0002-9939-1976-0409340-X

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DOI:
https://doi.org/10.1090/S0002-9939-1982-0647887-4

Article copyright:
© Copyright 1982
American Mathematical Society