The least nonzero digit of \(n!\) in base \(12\). (English) Zbl 1249.11044

Deshouillers, Jean-Marc; Ruzsa, Imre Z.

Publ. Math. Debr. 79, No. 3-4, 395-400 (2011).

Summary: We positively answer a question raised by the first author and prove that, for \(1 \leq a \leq 11\), the sequence \(\{n:\ell_{12}(n!)=a\}\) has an asymptotic density, which is \(1/2\) if \(a=4\) or \(a=8\) and \(0\) otherwise; here \(\ell_{b}(m)\) denotes the least nonzero digit of \(m\) in base \(b\).

MSC:

11B85	Automata sequences
11B05	Density, gaps, topology
11A63	Radix representation; digital problems

Keywords:

digit; factorial; automata; density