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PreprintCC BY 4.0arXiv

Tribonacci numbers that are palindromic concatenations of two distinct repdigits

  • Khady Faye
  • Bernadette Faye
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Abstract

Let (Tn)n≥1 be the Tribonacci sequence, defined by T1=T2=1, T3=2, and Tn=Tn−1+Tn−2+Tn−3 for n≥4. In this paper, we study the Tribonacci numbers whose decimal representation is a palindromic concatenation of two distinct repdigits, that is, numbers of the shape d1⋯ d1 d2⋯ d2 d1⋯ d1̅ with 1≤ d1≤9, 0≤ d2≤9, d1≠ d2. We prove that no Tribonacci number is a palindromic concatenation of two distinct repdigits. The proof combines lower bounds for linear forms in logarithms, the Baker-Davenport reduction method, and a finite computational verification.

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Cite

BibTeXRIS
BibTeX
@misc{faye2026tribonacci,
  title = {{Tribonacci numbers that are palindromic concatenations of two distinct repdigits}},
  author = {Khady Faye and Bernadette Faye},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15770},
  eprint = {2610.15770},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15770},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Tribonacci numbers that are palindromic concatenations of two distinct repdigits
AU  - Khady Faye
AU  - Bernadette Faye
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15770
UR  - https://arxiv.org/abs/2610.15770
AB  - Let (T_n)_n≥1 be the Tribonacci sequence, defined by T_1=T_2=1, T_3=2, and T_n=T_n−1+T_n−2+T_n−3 for n≥4. In this paper, we study the Tribonacci numbers whose decimal representation is a palindromic concatenation of two distinct repdigits, that is, numbers of the shape d_1⋯ d_1 d_2⋯ d_2 d_1⋯ d_1̅ with 1≤ d_1≤9, 0≤ d_2≤9, d_1≠ d_2. We prove that no Tribonacci number is a palindromic concatenation of two distinct repdigits. The proof combines lower bounds for linear forms in logarithms, the Baker-Davenport reduction method, and a finite computational verification.
ER  -