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arXiv · 1712.08666

Modular periodicity of the Euler numbers and a sequence by Arnold

Sanjay Ramassamy
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Abstract

For any positive integer $q$, the sequence of the Euler up/down numbers reduced modulo $q$ was proved to be ultimately periodic by Knuth and Buckholtz. Based on computer simulations, we state for each value of $q$ precise conjectures for the minimal period and for the position at which the sequence starts being periodic. When $q$ is a power of $2$, a sequence defined by Arnold appears, and we formulate a conjecture for a simple computation of this sequence.

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Sanjay Ramassamy. 2017-12-22. Modular periodicity of the Euler numbers and a sequence by Arnold. https://doi.org/10.1007/s40598-018-0079-0

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