Linking the Calkin–Wilf and Stern–Brocot trees

Abstract

Links between the Calkin–Wilf tree and the Stern–Brocot tree are discussed answering the questions: What is the j th vertex in the n th level of the Calkin–Wilf tree? and Where is the vertex r s located in the Calkin–Wilf tree? A simple mechanism is described for converting the j th vertex in the n th level of the Calkin–Wilf tree into the j th entry in the n th level of the Stern–Brocot tree. We also provide a simple method for evaluating terms in the Hyperbinary sequence thus answering a challenge raised in Quantum in September 1997. We also examine successors and predecessors in both trees.