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Palindromes in linear recurrence sequences

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Abstract

We prove that for any base \(b\ge 2\) and for any linear homogeneous recurrence sequence \(\{a_n\}_{n\ge 1}\) satisfying certain conditions, there exits a positive constant \(c>0\) such that \(\# \{n\le x:\ a_n \;\text{ is} \text{ palindromic} \text{ in} \text{ base}\; b\} \ll x^{1-c}\).

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Acknowledgments

We thank the referees for comments which improved the quality of this paper. F.L. worked on this paper during a visit to the Departamento de Matemáticas of the UAM in April of 2012. He thanks the people of this institution for their hospitality. F.L. was also supported in part by project PAPIIT IN 104512 and a Marcos Moshinsky Fellowship. J.C. was supported by the Spanish projects MTM-2011-22851 and SEV-2011-0087.

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Authors and Affiliations

  1. Departamento de Matemáticas, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Universidad Autónoma de Madrid, 28049 , Madrid, Spain

    Javier Cilleruelo & Rafael Tesoro

  2. Fundación Marcos Moshinsky, Instituto de Ciencias Nucleares UNAM, Circuito Exterior, C.U., Apdo. Postal 70-543, 04510 , Mexico, D.F., Mexico

    Florian Luca

Authors
  1. Javier Cilleruelo
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  2. Rafael Tesoro
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  3. Florian Luca
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Correspondence to Florian Luca.

Additional information

Communicated by J. Schoißengeier.

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Cilleruelo, J., Tesoro, R. & Luca, F. Palindromes in linear recurrence sequences. Monatsh Math 171, 433–442 (2013). https://doi.org/10.1007/s00605-013-0477-2

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  • DOI: https://doi.org/10.1007/s00605-013-0477-2

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