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On a problem of Granville and Zhu Regarding Pascal's triangle

Part of: Sequences and sets

Published online by Cambridge University Press:  26 February 2010

Yossi Moshe
Yossi Moshe
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel. E-mail: moshcy@cs.bgu.ac.il
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Abstract

Let A⊆ℕ, let p be a prime and w a word over ℤ pℤ ending with a non-zero digit. The relationship is investigated between the density of A. the length of w and the density of the set of numbers n for which the base p expansion of ends with w0n for some a ∈ A. Also considered is the analogous problem on Pascal's triangle. This leads in particular to answering a question of Granville and Zhu [7] regarding the asymptotic frequency of sums of 3 squares in Pascal's triangle.

MSC classification

Secondary: 11B65: Binomial coefficients; factorials; $q$-identities
Type
Research Article
Information
Mathematika , Volume 51 , Issue 1-2 , December 2004 , pp. 63 - 82
Copyright
Copyright © University College London 2004

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