Predictable Regular Continued Cotangent Expansions

Abstract

Le hme r called the x;s complete cotangents a nd the n;s incomplete or partial cotangents. He did not find a ny combination of familiar constant s whose regular co ntinued co tange nt ex pansion was in any way predic ta ble . He re we present an infinite seq ue nce of quadrati c irrationals with the prope rl y tha t eac h me mber of the seq ue nce has a predic table regular continued cota nge nt expa ns ion.