Mike Winkler, Ph.D.

Admissible qx+1 Sequences, Semiconvergents, and Rational Catalan Numbers

Let $q\geq3$ be odd and put $m_r=\lfloor r\log_2q\rfloor$. We count parity sequences with exactly $r$ entries equal to $1$ for which the coefficient in the $qx+1$ iteration first drops below $1$ at step $m_r+1$. Their number $a_q(r)$ also counts the corresponding residue classes modulo $2^{m_r+1}$. By classifying incre...