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The sum of a digitaddition series


Author: Kenneth B. Stolarsky
Journal: Proc. Amer. Math. Soc. 59 (1976), 1-5
MSC: Primary 10A30
DOI: https://doi.org/10.1090/S0002-9939-1976-0409340-X
MathSciNet review: 0409340
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Abstract: Let $ B(x)$ be the number of ones in the binary expansion of $ x$. A ``digitaddition series'' is a sequence $ {y_1} < {y_2} < {y_3} < \ldots $, where $ {y_1}$ is a given positive integer and $ {y_{n + 1}} = {y_n} + B({y_n})\;{\text{for}}\;n = 1,2, \ldots $. Various questions involving the $ {y_m}$ are studied; in particular, the asymptotic result $ {y_m} \sim (m\log m)/(2\log 2)$ is proved.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0409340-X
Keywords: Binary expansion, digitaddition series, self-number
Article copyright: © Copyright 1976 American Mathematical Society

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