Results 1 to 10 of about 33 (30)
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.,
JOSÉ L Herrera +2 more
exaly +3 more sources
On b-repdigit polygonal numbers [PDF]
Notes on Number Theory and Discrete MathematicsWe 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 +2 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 +1 more source
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 +1 more source
Repdigits as difference of two Fibonacci or Lucas numbers
Математичні Студії, 2021 In the present study we investigate all repdigits which are expressed as a difference of two Fibonacci or Lucas numbers. We show that if $F_{n}-F_{m}$ is a repdigit, where $F_{n}$ denotes the $n$-th Fibonacci number, then $(n,m)\in \{(7,3),(9,1),(9,2 ...
P. Ray, K. Bhoi
doaj +1 more source
Solutions of the Diophantine Equations Br = Js + Jt and Cr = Js + Jt
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br = Js + Jt and Cr = Js + Jt are completely solved. The solutions rely basically on Matveev’s theorem on linear forms in logarithms of algebraic numbers and a procedure of reducing the upper bound due to Dujella
Ahmed Gaber +2 more
wiley +1 more source
Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences
Mathematics, 2023 In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the k-generalized Fibonacci sequence which are almost repdigits. In particular, we find all k-
Alaa Altassan, Murat Alan
doaj +1 more source
Almost repdigits in balancing and Lucas-balancing sequences [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the balancing and Lucas-balancing sequences which are almost repdigits.
Manasi K. Sahukar, Hussain Basha
doaj +1 more source
On repdigits as product of $k$-Fibonacci and $k$-Lucas numbers [PDF]
Mathematica BohemicaFor an integer $k\geq2$, let $(F_n^{(k)})_{n\geq-(k-2)}$, $(L_n^{(k)})_{n \geq-(k-2)}$ be $k$-Fibonacci and $k$-Lucas sequences, respectively. For these sequences the first $k$ terms are $0,\ldots,0,1$ and $0,\ldots,0,2,1$, respectively, and each term ...
Safia Seffah +2 more
doaj +1 more source
Repdigits as Euler functions of Lucas numbers
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. +3 more
doaj +1 more source