Results 31 to 40 of about 2,080 (215)
Three new classes of binomial Fibonacci sums [PDF]
Transactions on CombinatoricsIn this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients. One particular result is linked to a problem proposal recently published in the journal The Fibonacci Quarterly.
Robert Frontczak
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The limit of reciprocal sum of some subsequential Fibonacci numbers
AIMS Mathematics, 2021 This paper deals with the sum of reciprocal Fibonacci numbers. Let $ f_0 = 0 $, $ f_1 = 1 $ and $ f_{n+1} = f_n+f_{n-1} $ for any $ n\in\mathbb{N} $. In this paper, we prove new estimates on $ \sum\limits^\infty_{k = n}\frac{1}{f_{mk-\ell}} $, where ...
Ho-Hyeong Lee, Jong-Do Park
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Divisibility of Fibonomial coefficients in terms of their digital representations and applications
AIMS Mathematics, 2022 We give a characterization for the integers $ n \geq 1 $ such that the Fibonomial coefficient $ {pn \choose n}_F $ is divisible by $ p $ for any prime $ p \neq 2, 5 $.
Phakhinkon Napp Phunphayap +1 more
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Fibonacci Numbers and Identities
The Fibonacci Quarterly, 2013 By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph associated to the recurrence relation.
Lang, Cheng Lien, Lang, Mong Lung
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Perfect numbers and Fibonacci primes (I) [PDF]
International Journal of Number Theory, 2014 In this paper, we introduce the concept of F-perfect number, which is a positive integer n such that ∑d|n,d<n d2 = 3n. We prove that all the F-perfect numbers are of the form n = F2k-1 F2k+1, where both F2k-1 and F2k+1 are Fibonacci primes. Moreover, we obtain other interesting results and raise a new conjecture on perfect numbers.
Tianxin Cai, Deyi Chen, Yong Zhang
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Analysis of a Nature-Inspired Shape for a Vertical Axis Wind Turbine
Applied Sciences, 2022 Wind energy is gaining special interest worldwide due to the necessity of reducing pollutant emissions and employ renewable resources. Traditionally, horizontal axis wind turbines have been employed but certain situations require vertical axis wind ...
Javier Blanco Damota +5 more
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Discrete Mathematics, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Types of Distance Fibonacci Numbers Generated by Number Decompositions
Journal of Applied Mathematics, 2014 We introduce new types of distance Fibonacci numbers which are closely related with number decompositions. Using special decompositions of the number n we give a sequence of identities for them.
Anetta Szynal-Liana +2 more
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Some results on one type of graph family with some special number sequences
AKCE International Journal of Graphs and Combinatorics, 2020 In this study, we introduce a new graph family. Then, we calculate eigenvalues of the adjacency and the Laplacian matrix of this graph family. Moreover, we show that the perfect matching number of this graph family equals to special second order ...
Emrullah Kirklar +2 more
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CAAI Transactions on Intelligence Technology, EarlyView.Abstract Life expectancy has improved with new‐age technologies and advancements in the healthcare sector. Though artificial intelligence (AI) and the Internet of Things (IoT) are revolutionising smart healthcare systems, security of the healthcare data is always a concern.
Shaiju Panchikkil +4 more
wiley +1 more source