H. Möller, Über Hasses Verallgemeinerung des Syracuse-Algorithmus (Kakutani's Problem), Acta Arith., 34 (1978) 219--226. This paper claims A. Fraenkel checked that for all , a result in error [32]. In a note added in proof it asserts the proofs of Terras [67] are faulty. They seem essentially correct to me, and Terras [68] supplies elided details.