Michael Drmota and Christian Krattenthaler

A joint central limit theorem for the sum-of-digits function, and asymptotic divisibility of Catalan-like sequences

(11 pages)

Abstract. We prove a central limit theorem for the joint distribution of sq(Ajn), 1 <= j <= d, where sq denotes the sum-of-digits function in base q and the Aj's are positive integers relatively prime to q. We do this in fact within the framework of quasi-additive functions. As application, we show that most elements of "Catalan-like" sequences - by which we mean integer sequences defined by products/quotients of factorials - are divisible by any given positive integer.

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