Binary digit distribution over naturally defined sequences
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- by D. J. Newman and Morton Slater PDF
- Trans. Amer. Math. Soc. 213 (1975), 71-78 Request permission
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
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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.
P. Erdös, On the density of abundant numbers, J. London Math. Soc. 9 (1934), 278-282.
E. Landau, Elementare Zahlentheorie, Teubner, Leipzig, 1927; English transl., Chelsea, New York, 1958. MR 19, 1159.
- Donald J. Newman, On the number of binary digits in a multiple of three, Proc. Amer. Math. Soc. 21 (1969), 719–721. MR 244149, DOI 10.1090/S0002-9939-1969-0244149-8
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 213 (1975), 71-78
- MSC: Primary 10K10
- DOI: https://doi.org/10.1090/S0002-9947-1975-0384734-3
- MathSciNet review: 0384734