Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the distribution of self-numbers

Author: U. Zannier
Journal: Proc. Amer. Math. Soc. 85 (1982), 10-14
MSC: Primary 10A30
MathSciNet review: 647887
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Abstract: Self-numbers are those integers which cannot be expressed as $ a + f(a)$, where $ f(a)$ denotes the sum of the digits of $ a$ in a given scale. Here I prove that the number of self-numbers less than or equal to a large number $ x$ equals $ Lx + O({\log ^2}x)$, where $ L$ is a strictly positive constant.

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Article copyright: © Copyright 1982 American Mathematical Society