On Generalized Cullen and Woodall Numbers That are Also Fibonacci Numbers
نویسنده
چکیده
The m-th Cullen number Cm is a number of the form m2 m + 1 and the m-th Woodall number Wm has the form m2 m − 1. In 2003, Luca and Stănică proved that the largest Fibonacci number in the Cullen sequence is F4 = 3 and that F1 = F2 = 1 are the largest Fibonacci numbers in the Woodall sequence. A generalization of these sequences is defined by Cm,s = ms m+1 and Wm,s = ms m−1, for s > 1. In this paper, we search for Fibonacci numbers belonging to these generalized Cullen and Woodall sequences.
منابع مشابه
Fibonacci s-Cullen and s-Woodall Numbers
The m-th Cullen number Cm is a number of the form m2 m + 1 and the m-th Woodall number Wm has the form m2 m − 1. In 2003, Luca and Stănică proved that the largest Fibonacci number in the Cullen sequence is F4 = 3 and that F1 = F2 = 1 are the largest Fibonacci numbers in the Woodall sequence. Very recently, the second author proved that, for any given s > 1, the equation Fn = ms m ± 1 has only f...
متن کاملCullen Numbers in Binary Recurrent Sequences
In this paper, we prove that the generalized Cullen numbers, Cn(s, l) := sn ·2+ l, where l is an integer and s := (sn)n≥0 is a sequence of integers satisfying log |sn| < 2n−1 + O(1), occur only finitely many times in binary recurrent sequences (un)n≥0 whose characteristic roots are quadratic units and that satisfy some additional conditions. We also generalize this result in some sense to show ...
متن کاملEnergy of Graphs, Matroids and Fibonacci Numbers
The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.
متن کاملCoefficient Bounds for Analytic bi-Bazileviv{c} Functions Related to Shell-like Curves Connected with Fibonacci Numbers
In this paper, we define and investigate a new class of bi-Bazilevic functions related to shell-like curves connected with Fibonacci numbers. Furthermore, we find estimates of first two coefficients of functions belonging to this class. Also, we give the Fekete-Szegoinequality for this function class.
متن کاملOn generalized fuzzy numbers
This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...
متن کامل