Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.8

Largest Values of the Stern Sequence, Alternating Binary Expansions and Continuants

Roland Paulin
Max-Planck-Institut für Mathematik
Vivatsgasse 7
D-53111, Bonn


We study the largest values of the rth row of Stern's diatomic array. In particular, we prove some conjectures of Lansing. Our main tool is the connection between the Stern sequence, alternating binary expansions, and continuants. This allows us to reduce the problem of ordering the elements of the Stern sequence to the problem of ordering continuants. We describe an operation that increases the value of a continuant, allowing us to reduce the problem of largest continuants to ordering continuants of very special shape. Finally, we order these special continuants using some identities and inequalities involving Fibonacci numbers.

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(Concerned with sequence A002487.)

Received September 13 2016; revised version received November 15 2016. Published in Journal of Integer Sequences, December 27 2016.

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