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Abstract
Stern's diatomic sequence appeared in print in 1858 and has been the subject of numerous papers since. Our goal is to present many of these properties, both old and new. We present a large set of references and, for many properties, we supply simple proofs or ones that complement existing proofs. Among the topics covered are what these numbers count (hyperbinary representations) and the sequence's surprising parallels with the Fibonacci numbers. Quotients of consecutive terms lead to an enumeration of the rationals. Other quotients lead to a map from dyadic rationals to the rationals whose completion is the inverse of Minkowski's? function. Along the way, we get a distant view of fractals and the Riemann hypothesis as well as a foray into random walks on graphs in the hyperbolic plane.
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Sam Northshield
SAM NORTHSHIELD received his B.S. from Marlboro College in 1982 and his Ph.D. from the University of Rochester in 1989. Since then he has been teaching at SUNY-Plattsburgh interrupted only by several visiting positions in Minnesota and Vermont. He is pleased to write a MONTHLY article that evolved, however obliquely, from his first two mathematical loves: continued fractions and the modular figure.