Results 21 to 30 of about 198 (98)
Tribonacci numbers that are concatenations of two repdigits. [PDF]
Rev R Acad Cienc Exactas Fis Nat A Mat, 2020 Let $ (T_{n})_{n\ge 0} $ be the sequence of Tribonacci numbers defined by $ T_0=0 $, $ T_1=T_2=1$, and $ T_{n+3}= T_{n+2}+T_{n+1} +T_n$ for all $ n\ge 0 $. In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two ...
Ddamulira M.
europepmc +6 more sources
On Sierpiński and Riesel Repdigits and Repintegers
For positive integers $b\geq 2 ...
Bispels, Chris +6 more
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Repdigits as sums of four Pell numbers [PDF]
Boletín de la Sociedad Matemática Mexicana, 2018 Let \( (P_m)_{m\ge 0} \) be the sequence of \textit{Pell numbers} given by the linear recurrence; \( P_0=0 \), \( P_1=1 \), and \( P_{m+2} = 2P_{m+1}+ P_m \) for all \( m\ge 0 \). In the paper under review, the authors prove the following theorem, which is the main result in the paper. Theorem 1. All nonnegative integer solutions \( (m_1, m_2, m_3, m_4,
Florian Luca +2 more
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Repdigits in generalized Pell sequences [PDF]
Archivum Mathematicum, 2020 In this paper, the authors study the \(k\)-generalized Pell sequence, which starts with \(0,\ldots,0,1\) and satisfies the recurrence \(P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)}\). They find all \(k\)-generalized Pell numbers which are repdigits, namely \(P_5^{(3)}=33\) and \(P_6^{(4)}=88\).
Bravo, Jhon J., Herrera, Jose L.
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Factorials as repdigits in base $b$ [PDF]
Notes on Number Theory and Discrete Mathematics, 2022 Let $b\in \left\{ 2,3, \ldots,9\right\}.$ In this paper, we show that the solutions of the equation $\left( x\right) _{b}=m! $ are $\left( 11\right) _{5}=3!, \left( 33\right) _{7}=\left( 44\right)_{5}=4!$, where $\left( x\right) _{b}$ has at least two digits.
Nurettin Irmak, Alain Togbé
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k-generalized Fibonacci numbers which are concatenations of two repdigits [PDF]
, 2021 We show that the k-generalized Fibonacci numbers that are concatenations of two repdigits have at most four ...
Alahmadi, Adel +7 more
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Padovan Numbers as Sum of Two Repdigits
Proceedings of the Bulgarian Academy of Sciences, 2023 Padovan sequence $$(P_{n})$$ is given by $$P_{n}=P_{n-2}+P_{n-3}$$ for $$n\geq3$$ with initial condition $$(P_{0},P_{1},P_{2})=(1,1,1)$$. A positive integer is called a repdigit if all of its digits are equal. In this study, we examine the terms of the Padovan sequence, which are the sum of two repdigits.
Duman, Merve Güney +5 more
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Curious Generalized Fibonacci Numbers
Mathematics, 2021 A generalization of the well-known Fibonacci sequence is the k−Fibonacci sequence whose first k terms are 0,…,0,1 and each term afterwards is the sum of the preceding k terms. In this paper, we find all k-Fibonacci numbers that are curious numbers (i.e.,
Jose L. Herrera +2 more
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Can a Lucas number be a sum of three repdigits? [PDF]
, 2020 summary:We give the answer to the question in the title by proving that \begin{equation*} L_{18} = 5778 = 5555 + 222 + 1 \end{equation*} is the largest Lucas number expressible as a sum of exactly three repdigits.
Adegbindin, Chèfiath A., Togbé, Alain
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Fibonacci numbers which are concatenations of two repdigits [PDF]
, 2021 We show that the only Fibonacci numbers that are concatenations of two repdigits are 13, 21, 34, 55, 89, 144, 233 ...
Alahmadi, Adel +7 more
core +1 more source