Results 31 to 40 of about 83 (68)

Repdigits Base $b$ as Difference of Two Fibonacci Numbers

Journal of Mathematical Study, 2022
Summary: In this paper, we find all repdigits expressible as difference of two Fibonacci numbers in base \(b\) for \(2\leq b\leq10\). The largest repdigits in base \(b\), which can be written as difference of two Fibonacci numbers are \[ \begin{aligned} &F_9-F_4=34-3=31=(11111)_2, &&F_{14}-F_7=377-13=364=(111111)_3,\\ &F_{14}-F_7=377-13=364=(222)_4 ...
Siar, Zafer, Erduvan, Fatih, Keskin, Refik, Keskin, Refik   +3 more
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Repdigits in Euler functions of associated pell numbers

Proceedings - Mathematical Sciences, 2020
Let \(\{Q_n\}\) denotes the sequence of numbers defined by \[ Q_0=1;~Q_1=1;~Q_{n+1}=2Q_n+Q_{n-1},~n\geq 1. \] Using elementary number theoretic notions, the following main result is proved: Theorem. Let \(d\in \{1,\ldots,9\}\) and \(m\in \mathbb{N}\).
Panda, G. K., Sahukar, M. K.
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Repdigits in Narayana's Cows Sequence and their Consequences

, 2020
Narayana's cows sequence satisfies the third-order linear recurrence relation $N_n=N_{n-1}+N_{n-3}$ for $n \geq 3$ with initial conditions $N_0=0$ and $N_1=N_2=1$. In this paper, we study $b$-repdigits which are sums of two Narayana numbers. We explicitly determine these numbers for the bases $2\le b\leq100$ as an illustration.
Bravo, Jhon J., Das, Pranabesh, Guzmán, Sergio   +2 more
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Narayana numbers as products of three repdigits in base g

Acta et Commentationes Universitatis Tartuensis de Mathematica, 2023
In this paper, we show that there are only finitely many Narayana's numbers which can be written as a product of three repdigits in base g with g >= 2. Moreover, for 2 <= g <= 10, we determine all these numbers.    
Pagdame Tiebekabe, Kossi Richmond KAKANOU, Hamid Ben Yakkou   +2 more
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On repdigits powers in base beta

Lietuvos matematikos rinkinys, 2022
The article presents formulas for powers of repdigits in the different numeral systems. This task can be used as an exercise for computer science students to help them master the corresponding mathematical apparatus.
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Padovan numbers that are concatenations of two distinct repdigits [PDF]

Mathematica Slovaca, 2020
Abstract Let ( P n ) n ≥0 be the sequence of Padovan numbers defined by P
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On Sierpiński and Riesel Repdigits and Repintegers

For positive integers $b\geq 2 ...
Bispels, Chris, Cohen, Matthew, Harrington, Joshua, Lowrance, Joshua, Pontes, Kaelyn, Schaumann, Leif, Wong, Tony W. H.   +6 more
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Repdigits in k-generalized Pell sequence

, 2020
Let $k\geq 2$ and let $(P_{n}^{(k)})_{n\geq 2-k}$ be $k$-generalized Pell sequence defined by \begin{equation*}P_{n}^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+...+P_{n-k}^{(k)}\end{equation*} for $n\geq 2$ with initial conditions \begin{equation*}P_{-(k-2)}^{(k)}=P_{-(k-3)}^{(k)}=\cdot \cdot \cdot =P_{-1}^{(k)}=P_{0}^{(k)}=0,P_{1}^{(k)}=1.
Şiar, Zafer, Keskin, Refik
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Padovan numbers that are concatenations of two repdigits [PDF]

, 2020
Let $ (P_{n})_{n\ge 0} $ be the sequence of Padovan numbers defined by $ P_0=0 $, $ P_1 =1=P_2$, and $ P_{n+3}= P_{n+1} +P_n$ for all $ n\ge 0 $. In this paper, we find all Padovan numbers that are concatenations of two repdigits.
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Repdigits as sums of three Fibonacci numbers

Mathematical Communications, 2012
In this paper, we find all base 10 repdigits which are sums of three Fibonacci numbers.
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