Factoriangular numbers in balancing and Lucas-balancing sequence

Abstract

In this paper, we prove the nonexistence of factoriangular numbers in balancing and Lucas-balancing sequence.

On the Generalization of Factoriangular Numbers

“…In 2015, this number was named factoriangular, a contraction of the terms factorial and triangular [3]. A factoriangular number is a sum of a factorial and its corresponding triangular number and some recent studies were conducted on this relatively new sequence of numbers [3][4][5][6][7][8][9][10][11][12].…”

“…Luca, Odjoumani and Togbe [8] show that the only Pell factoriangular numbers are 2, 5, and 12 while Kafle, Luca and Togbe [9] show that the only Lucas factoriangular numbers are 1 and 2. In addition, Rayaguru, Odjoumani and Panda [10] prove that there is no factoriangular number in the sequence of balancing numbers, as well as in the sequence of Lucas-balancing numbers.…”

Solutions of the Diophantine Equations B r = J Gaber, Ahmed 2023Journal of Mathematics0000View full textAdd to dashboardCite

“…In [5], Erduvan and Keskin studied and determined Fibonacci numbers which are products of two balancing numbers. In [6], Rayaguru et al found the factoriangular numbers in the sequences of balancing and Lucas balancing numbers. In [7], Ddamulira obtained all the repdigits that can be written as sums of three balancing numbers.…”