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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$.

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

  • [1] L. Dickson, History of the theory of numbers. Vols. 1, 2, 3, Publ. no. 256, Carnegie Inst., Washington, D.C., 1919, 1920, 1923; reprint, Stechert, New York.
  • [2] P. Erdös, On the density of abundant numbers, J. London Math. Soc. 9 (1934), 278-282.
  • [3] E. Landau, Elementare Zahlentheorie, Teubner, Leipzig, 1927; English transl., Chelsea, New York, 1958. MR 19, 1159.
  • [4] D. J. Newman, On the number of binary digits in a multiple of three, Proc. Amer. Math. Soc. 21 (1969), 719-721. MR 0244149 (39:5466)

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Keywords: Binary digits, arithmetic progressions, sieving, abundant numbers
Article copyright: © Copyright 1975 American Mathematical Society

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