# 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 *s*_{q}(*A*_{j}n),
1 <= *j* <= *d*, where *s*_{q} denotes
the sum-of-digits function in base *q* and the
*A*_{j}'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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