Abstract
A repdigit is a positive integer that has only one distinct digit in its decimal expansion, i.e., a number of the form a(10^m-1)/9, for some mge 1 and 1 le a le 9. Let left( P_nright) _{nge 0} and left( E_nright) _{nge 0} be the sequence of Padovan and Perrin numbers, respectively. This paper deals with repdigits that can be written as the products of consecutive Padovan or/and Perrin numbers.
Highlights
A positive integer is called a repdigit if it has only one distinct digit in its decimal expansion
The Padovan and Perrin sequences are included in the OEIS [13] as the sequences A000931 and A001608, respectively
It is natural to ask what will happen if we consider Padovan and Perrin numbers
Summary
A positive integer is called a repdigit if it has only one distinct digit in its decimal expansion. Let (En)n≥0 be the Perrin sequence following the same recursive pattern as the Padovan sequence, but with initial conditions E0 = 2, E1 = 0, and E2 = 1. Marques and the second author [9] studied repdigits as products of consecutive Fibonacci numbers. Irmak and the second author [5] studied repdigits as products of consecutive Lucas numbers. Rayaguru and Panda [11] studied repdigits as products of consecutive Balancing and Lucas-Balancing numbers. It is natural to ask what will happen if we consider Padovan and Perrin numbers. In this paper, we investigate repdigits which can be written as the product of consecutive Padovan or/and Perrin numbers. Computations are done with the help of a computer program in Maple
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