Was there a custom to read the Torah once every three years?
The Talmud (Megillah 29b) says that in the Land of Israel it was customary to read through the Torah every three years. There are traditional subdivisions of the Torah into 153, 155, or 167 parts, called Sedarim; 153 or 155 corresponds to a three-year cycle, but 167 is too few for a 3.5-year cycle. Good editions of the Torah indicate where the Sedarim begin, but opinions differ as to whether the three-year cycle began in Nisan or in Tishrei. Scholars have tried to reconstruct the readings from the Prophets that were associated with the Sedarim. A major work on this topic is J.Mann, The Bible as Read and Preached in the Old Synagogue, Cincinnati, Ohio, 1940 and 1966 (the second volume was coauthored by I.Sonne), which covers the first 106 Sedarim.