On sequences resulting from iteration of modified quadratic and palindromic mappings

AbstractBlanchard and Fabre (1994) have considered description of symbolic systems by sequences obtained by iteration of two mappings gj and dj, defined by gj(u) = u[u]j and dj = u[u]Rj, where the word [u]j is obtained from a word u by removing the last j symbols. They stated a conjecture that the iteration of dj results in an automatic sequence. We prove here that dj is, while gj is not, a 2-automatic sequence. Our result is obtained by investigation of two wider classes of sequences