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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Binary digit distribution over naturally defined sequences


Authors: D. J. Newman and Morton Slater
Journal: Trans. Amer. Math. Soc. 213 (1975), 71-78
MSC: Primary 10K10
MathSciNet review: 0384734
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Abstract: In a previous paper the first author showed that multiples of 3 prefer to have an even number of ones in their binary digit expansion. In this paper it is shown that in some general classes of naturally defined sequences, the probability that a member of a particular sequence has an even number of ones in its binary expansion is $ 1/2$.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0384734-3
Keywords: Binary digits, arithmetic progressions, sieving, abundant numbers
Article copyright: © Copyright 1975 American Mathematical Society