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Proceedings of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

  • [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] K. B. Stolarsky, The sum of a digitaddition series, Proc. Amer. Math. Soc. 59 (1976), 1-5. MR 0409340 (53:13099)

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Article copyright: © Copyright 1982 American Mathematical Society

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