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arXiv · 1005.3624

On Arithmetic Progressions in Recurrences - A new characterization of the Fibonacci sequence

Akos Pinter·Volker Ziegler
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Abstract

We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic progressions is also given.

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Akos Pinter, Volker Ziegler. 2010-05-20. On Arithmetic Progressions in Recurrences - A new characterization of the Fibonacci sequence. https://arxiv.org/abs/1005.3624

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