Results 31 to 40 of about 688 (71)
The density of numbers $n$ having a prescribed G.C.D. with the $n$th Fibonacci number [PDF]
, 2018 For each positive integer $k$, let $\mathscr{A}_k$ be the set of all positive integers $n$ such that $\gcd(n, F_n) = k$, where $F_n$ denotes the $n$th Fibonacci number.
Sanna, Carlo, Tron, Emanuele
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On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers
Discussiones Mathematicae - General Algebra and Applications, 2020 In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.
Dutta Utkal Keshari, Ray Prasanta Kumar
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, 2006 In this work, we introduce another extension U of the 3n+1 function to the real line. We propose a conjecture about the U-trajectories that generalizes the famous 3n+1 (or Collatz) conjecture.
Konstadinidis, Pavlos B.
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On Quaternion-Gaussian Fibonacci Numbers and Their Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients.
Halici Serpil, Cerda-Morales Gamaliel
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On r-Jacobsthal and r-Jacobsthal-Lucas Numbers
Annales Mathematicae Silesianae, 2023 Recently, Bród introduced a new Jacobsthal-type sequence which is called r-Jacobsthal sequence in current study. After defining the appropriate r-Jacobsthal–Lucas sequence for the r-Jacobsthal sequence, we obtain some properties of these two sequences ...
Bilgici Göksal, Bród Dorota
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One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers
Annales Mathematicae Silesianae, 2023 In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover,
Bród Dorota +2 more
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On Cauchy Products of q−Central Delannoy Numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this study, we have examined q− central Delannoy numbers and their Cauchy products. We have given some related equalities using the properties of recurrence relations.
Halıcı Serpil
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Analytic Properties of the Apostol-Vu Multiple Fibonacci Zeta Functions
Discussiones Mathematicae - General Algebra and Applications, 2020 In this note we study the analytic continuation of the Apostol-Vu multiple Fibonacci zeta functions ζAVF,k(s1,…,sk,sk+1)=∑1 ...
Dutta Utkal Keshari, Ray Prasanta Kumar
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On the reciprocal sum of the fourth power of Fibonacci numbers
Open Mathematics, 2022 Let fn{f}_{n} be the nnth Fibonacci number with f1=f2=1{f}_{1}={f}_{2}=1. Recently, the exact values of ∑k=n∞1fks−1⌊{\left({\sum }_{k=n}^{\infty }\frac{1}{{f}_{k}^{s}}\right)}^{-1}⌋ have been obtained only for s=1,2s=1,2, where ⌊x⌋\lfloor x\
Hwang WonTae +2 more
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The extensibility of the Diophantine triple {2, b, c}
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple.
Adžaga Nikola +2 more
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