Results 1 to 10 of about 133 (87)

On some polynomial values of repdigit numbers [PDF]

Electronic Notes in Discrete Mathematics, 2013
Let \[ f_{k,m}(x)=\frac{x(x+1)\ldots(x+k-2)((m-2)x+k+2-m)}{k!} \] be the \(m\)th order \(k\)-dimensional polygonal number, where \(k\geq 2\) and \(m\geq 3\) are fixed integers. As special cases for \(f_{k,3}\) we get the binomial coefficient \(\binom{x+k-1}{k}\), for \(f_{2,m}(x)\) and \(f_{3,m}(x)\) we have the corresponding polygonal and pyramidal ...
Nora Varga, Tunde Kovacs
exaly   +15 more sources

On b-repdigit polygonal numbers [PDF]

Notes on Number Theory and Discrete Mathematics
We prove a finiteness theorem concerning repdigits in base b≥2 represented by a fixed quadratic polynomial. We also show that there is a finite number of polygonal numbers that are also b-repdigits for all b≥2 provided that (b,s) ∈\ {((8(s-2)/(s-4))(d+1),
Adriana Mora, Eric Bravo
exaly   +3 more sources

Repdigits as Euler functions of Lucas numbers [PDF]

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
We prove some results about the structure of all Lucas numbers whose Euler function is a repdigit in base 10. For example, we show that if Ln is such a Lucas number, then n < 10111 is of the form p or p2, where p3 | 10p-1 -1.
Bravo Jhon J., Faye Bernadette, Luca Florian, Tall Amadou   +3 more
doaj   +3 more sources

Repdigits as products of two Fibonacci or Lucas numbers

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2020
Let \( (F_n)_{n\ge 0} \) and \( (L_n)_{n\ge 0} \) be the sequences of Fibonacci and Lucas numbers given by \( F_0=0, ~ F_1=1, ~ L_0=2, ~L_1=1 \), \( F_{n+2}=F_{n+1}+F_n \), and \( L_{n+2}=L_{n+1}+L_n \) for all \( n\ge 0 \), respectively. A repdigit is a positive integer \( N \) that has only one distinct digit when written in its decimal expansion ...
Fatih Erduvan, Refik Keskin
exaly   +4 more sources

Lucas sequences and repdigits [PDF]

Mathematica Bohemica, 2022
Let $(G_n)_{n \geq1}$ be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are $\{U_n\}$ and $\{V_n\}$, respectively.
Hayder Raheem Hashim, Szabolcs Tengely
doaj   +3 more sources

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

Repdigits as sums of three Padovan numbers. [PDF]

Bol Soc Mat Mex, 2020
AbstractLet $$ \{P_{n}\}_{n\ge 0} $${Pn}n≥0 be the sequence of Padovan numbers defined by $$ P_0=0 $$P0=0, $$ P_1 =1=P_2$$P1=1=P2, and $$ P_{n+3}= P_{n+1} +P_n$$Pn+3=Pn+1+Pn for all $$ n\ge 0 $$n≥0. In this paper, we find all repdigits in base 10 which can be written as a sum of three Padovan numbers.
Ddamulira M.
europepmc   +8 more sources

Repdigits in the base $b$ as sums of four balancing numbers [PDF]

Mathematica Bohemica, 2021
The sequence of balancing numbers $(B_n)$ is defined by the recurrence relation $B_n=6B_{n-1}-B_{n-2}$ for $n\geq2$ with initial conditions $B_0=0$ and $B_1=1.$ $B_n$ is called the $n$th balancing number. In this paper, we find all repdigits in the base $
Refik Keskin, Fatih Erduvan
doaj   +2 more sources

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.,
Jhon Jairo Bravo Grijalba, José L Herrera, Carlos Gomez   +2 more
exaly   +3 more sources

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.
openaire   +2 more sources