Activity: Talk or presentation › Oral presentation
Description
For an integer k greater than 1, k-regular sequences were defined by Allouche and Shallit. We study two of the "simplest" such sequences, which are well-known: (1.) the discrepancy of the van der Corput sequence, and (2.) the number of odd entries in a given row of Pascal's triangle. In the first case, a Gaussian behaviour is known by previous results of Drmota, Larcher, and Pillichshammer; the second case gives rise to a constant (the Stolarsky--Harborth constant) whose precise value is still unknown. We give an overview of these topics, and point out possible paths towards progress on these topics.