Number of odd binomial coefficients
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- by Heiko Harborth PDF
- Proc. Amer. Math. Soc. 62 (1977), 19-22 Request permission
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
- N. J. Fine, Binomial coefficients modulo a prime, Amer. Math. Monthly 54 (1947), 589–592. MR 23257, DOI 10.2307/2304500
- Heiko Harborth, Über die Teilbarkeit im Pascal-Dreieck, Math.-Phys. Semesterber. 22 (1975), 13–21 (German). MR 384676
- David Singmaster, Notes on binomial coefficients. III. Any integer divides almost all binomial coefficients, J. London Math. Soc. (2) 8 (1974), 555–560. MR 396285, DOI 10.1112/jlms/s2-8.3.555 K. B. Stolarsky, Digital sums and binomial coefficients, Notices Amer. Math. Soc. 22 (1975), A-669. Abstract #728-A7.
- 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 439735, DOI 10.1137/0132060
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 19-22
- MSC: Primary 10A20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0429714-1
- MathSciNet review: 0429714