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Proceedings of the American Mathematical Society
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 | References | Similar Articles | Additional Information

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?)

  • [1] N. J. Fine, Binomial coefficients modulo a prime, Amer. Math. Monthly 54 (1947), 589-592. MR 9, 331. MR 0023257 (9:331b)
  • [2] H. Harborth, Über die Teilbarkeit im Pascal-Dreieck, Math.-Phys. Semesterber. 22 (1975), 13-21. MR 0384676 (52:5549)
  • [3] D. Singmaster, Notes on binomial coefficients. III: Any integer divides almost all binomial coefficients, J. London Math. Soc. (2) 8 (1974), 555-560. MR 0396285 (53:153)
  • [4] K. B. Stolarsky, Digital sums and binomial coefficients, Notices Amer. Math. Soc. 22 (1975), A-669. Abstract #728-A7.
  • [5] -, Power and exponential sums of digital sums related to binomial coefficient parity, SIAM J. Appl. Math. (to appear). MR 0439735 (55:12621)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0429714-1
PII: S 0002-9939(1977)0429714-1
Article copyright: © Copyright 1977 American Mathematical Society