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Modular Periodicity of the Euler Numbers and a Sequence by Arnold

Modular Periodicity of the Euler Numbers and a Sequence by Arnold 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arnold Mathematical Journal Springer Journals

Modular Periodicity of the Euler Numbers and a Sequence by Arnold

Ramassamy, Sanjay
Arnold Mathematical Journal , Volume 3 (4) – Jan 22, 2018
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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute for Mathematical Sciences (IMS), Stony Brook University, NY
Subject
Mathematics; Mathematics, general
ISSN
2199-6792
eISSN
2199-6806
DOI
10.1007/s40598-018-0079-0
Publisher site
See Article on Publisher Site

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.

Journal

Arnold Mathematical Journal – Springer Journals

Published: Jan 22, 2018

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