学术报告：Automatic questions concerning the representation of n! in base b

 中科院数学与系统科学研究院

数学研究所

学术报告会

报告人：Prof. Jean-Marc Deshouillers(Bordeaux INP，France)

题  目：Automatic questions concerning the representation of n! in base b

时  间：10.23 (星期五) 上午10:00-11:00

地  点：数学院南楼N818室

摘要：

   We shall first recall a joint work with Florian Luca showing that the automaticity of the ``final non-zero digits” of n! written in base 2 leads to the density of the integers n for which n! is a sum of three squares, a conjecture of Luca and Shparlinsky.

    The sequence A008904 from the On-line Encyclopedia of Integers Sequences gives the“final non-zero digit”of n! written in the base 10, studied at least some fifty years ago by Kakutani. The comments on this entry indicate that this sequence, which contains only the four digits 2, 4, 6, 8 for $n\ge 2$, is an“automatic sequence”and the given computation illustrates the fact that the four above mentioned digits occur with the same asymptotic frequency.

    We shall present some results due to Imre Ruzsa and myself on the same question related to the base 12 (sequence A136698) where some special feature occurs. We shall also report on a joint work in progress, with Greg Dresden (W&L) and Shanta Laishram (ISI Delhi), concerning the case of a general base b.