Narayana's cows numbers which are concatenations of three repdigits in base ρ

2023/04/03 by Pagdame Tiebekabe, Tiebekabe, Pagdame, Kouèssi Norbert Adédji +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #11B39 #11D61 #11J86 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2304.00773

openalex publication_date 2023/04/03 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28

Abstract

Narayana's sequence is a ternary recurrent sequence defined by the recurrence relation N_n=N_n-1+N_n-3 with initial terms N₀=0 and N₁=N₂=N₃=1. Let ρ\geqslant2 be a positive integer. In this study, it is proved that the nth Narayana's number N_n which is concatenations of three repdigits in base ρ satisfies n<5.6⋅ 10⁴⁸⋅ log⁷ρ. Moreover, it is shown that the largest Narayana's number which is concatenations of three repdigits in base ρ with 1 \leqslant ρ\leqslant 10 is 58425=N₃₁=3332200₅=332223₇.

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• On Narayana numbers which are products of four b-repdigits with a consequence

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