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September 27, 2025Open Access

On b−repdigits which are sums of three Narayana numbers with a consequence

PTPagdame Tiebekabe SCS ́emou Diouf Cheikh SNSalifou Nikiema

Key Points

Brepdigits can be formed as sums of three Narayana numbers, expanding our understanding of number sequences.
The study includes bases ranging from 2 to 30, examining how they affect the representation of brepdigits.
Key methodologies involve lower bounds for linear forms in logs and Baker-Davenport methods in Diophantine equations.
This approach highlights the interaction between number theory and recurrence relations, leading to further research opportunities.

Abstract

The sequence known as Narayana’s cows sequence is defined by the thirdorder linear recurrence relation Nn = Nn−1 + Nn−3, for n ≥ 3, with the initial values given by N0 = N1 = N2 = 1. In this paper, we explore the class of numbers known as brepdigits that can be represented as the sum of three terms from this sequence. Specifically, we aim to identify all such numbers for bases in the range 2 ≤ b ≤ 30. Our approach relies on precise lower bounds for linear forms in logarithms, along with an enhanced version of the Baker-Davenport reduction method applied to Diophantine equations.

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