Repdigits as sums of three balancing numbers
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Mahadi Ddamulira
Abstract
Let {Bn}n≥0 be the sequence of Balancing numbers defined by B0 = 0, B1 = 1, and Bn+2 = 6Bn+1 − Bn for all n ≥ 0. In this paper, we find all repdigits in base 10 which can be written as a sum of three Balancing numbers.
This research was supported by the Austrian Science Fund (FWF) projects: F5510-N26 – Part of the special research program (SFB), “Quasi-Monte Carlo Methods: Theory and Applications” and W1230 – “Doctoral Program Discrete Mathematics”.
Communicated by Milan Paštéka
Acknowledgement
The author thanks the referee for the useful comments and suggestions that greatly improved the quality of presentation of the paper.
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© 2020 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- Recurrences for the genus polynomials of linear sequences of graphs
- The existence of states on EQ-algebras
- On sidon sequences of farey sequences, square roots and reciprocals
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- Refinement of fejér inequality for convex and co-ordinated convex functions
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- Coefficients problems for families of holomorphic functions related to hyperbola
- Triebel-Lizorkin capacity and hausdorff measure in metric spaces
- The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses
- On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers
- Density of summable subsequences of a sequence and its applications
- Rough weighted 𝓘-limit points and weighted 𝓘-cluster points in θ-metric space
- A note on cosine series with coefficients of generalized bounded variation
- Some geometric properties of the non-Newtonian sequence spaces lp(N)
- On sequence spaces defined by the domain of a regular tribonacci matrix
- Jointly separating maps between vector-valued function spaces
- Some fixed point theorems for multi-valued mappings in graphical metric spaces
- Monotone transformations on the cone of all positive semidefinite real matrices
- Locally defined operators in the space of Ck,ω-functions
- Some properties of D-weak operator topology
- Estimating the distribution of a stochastic sum of IID random variables
- An internal characterization of complete regularity
