Padovan numbers which are concatenations of three repdigits

2022/12/21 by Kisan Bhoi, Bhoi, Kisan, Prasanta Kumar Ray +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2212.10831

openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Padovan sequence is a ternary recurrent sequence defined by the recurrence relation P_n+3=P_n+1+P_n with initial terms P₀=P₁=P₂=1. In this study it is shown that 114,151,200,265,351,465,616,816,3329,4410,7739,922111 are the only Padovan numbers which are concatenations of three repdigits.

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