Some sequences related to circle rotations over simple quadratic irrationals turn up in the online encyclopaedia of integers sequences (OEIS). In this joint work with Robbert Fokkink some conjectures about A120243 are solved, using either automata theory or renormalization of circle rotations.

Reference to the paper this talk is based on: Henk Bruin and Robbert Fokkink On the records and zeros of a deterministic random walk, Advances in Applied Mathematics, 172 (2026), Paper No. 102963. ArXiv version: https://arxiv.org/abs/2503.11734

Link to A120243: https://oeis.org/A120243