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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The author acknowledges the support of the Fondation Simone et Cino Del Duca.
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Ramassamy, S. Modular Periodicity of the Euler Numbers and a Sequence by Arnold. Arnold Math J. 3, 519–524 (2017). https://doi.org/10.1007/s40598-018-0079-0
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DOI: https://doi.org/10.1007/s40598-018-0079-0