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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Number of odd binomial coefficients


Author: Heiko Harborth
Journal: Proc. Amer. Math. Soc. 62 (1977), 19-22
MSC: Primary 10A20
MathSciNet review: 0429714
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Abstract: Let $ F(n)$ denote the number of odd numbers in the first n rows of Pascal's triangle, and $ \theta = (\log 3)/\log 2)$. Then $ \alpha = \lim \sup F(n)/{n^\theta } = 1$, and $ \beta = \lim \inf F(n)/{n^\theta } = 0.812\;556\; \ldots .$


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

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  • [2] Heiko Harborth, Über die Teilbarkeit im Pascal-Dreieck, Math.-Phys. Semesterber. 22 (1975), 13–21 (German). MR 0384676
  • [3] David Singmaster, Notes on binomial coefficients. III. Any integer divides almost all binomial coefficients, J. London Math. Soc. (2) 8 (1974), 555–560. MR 0396285
  • [4] K. B. Stolarsky, Digital sums and binomial coefficients, Notices Amer. Math. Soc. 22 (1975), A-669. Abstract #728-A7.
  • [5] Kenneth B. Stolarsky, Power and exponential sums of digital sums related to binomial coefficient parity, SIAM J. Appl. Math. 32 (1977), no. 4, 717–730. MR 0439735

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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0429714-1
Article copyright: © Copyright 1977 American Mathematical Society