Modular periodicity of the Euler numbers and a sequence by Arnold

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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Contributor : Sanjay Ramassamy <>
Submitted on : Monday, January 22, 2018 - 3:47:16 PM
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Sanjay Ramassamy. Modular periodicity of the Euler numbers and a sequence by Arnold. Arnold Mathematical Journal, Springer, 2017, 3 (4), pp.519-524. ⟨hal-01689995⟩

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