Add to ORKGAbstract. We examine integer sequences G satisfying the Fibonacci recurrence relation Gn = Gn−1 + Gn−2 that also have the property that G ≡ 1, a, a2, a3,... (mod m) for some modulus m. We determine those moduli m for which these power Fibonacci sequences exist and the number of such sequences for a given m. We also provide formulas for the periods of these sequences, based on the period of the Fibonacci sequence F modulo m. Finally, we establish certain sequence/subsequence relationships between power Fibonacci sequences. 1
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
In this paper, we find patterns and count the number of distinct generalised Fibonacci sequences und...
centuries, as it seems there is no end to its many surprising properties. Of particular interest to ...
The purposes of this paper are; (a) to develop a relationship between subscripts of the symbols of F...
The purposes of this paper are; (a) to develop a relationship between subscripts of the symbols of F...
Abstract. The Fibonacci sequence U0 = 1, U1 = 5 and Un = 3 ·Un−1+Un−2 for n ≥ 2 yields a purely peri...
The Fibonacci numbers are defined by the recurrence f(n)= f(n-1)+f(n-2). The sequence f(n)mod m is p...
The Fibonacci numbers are defined by the recurrence f(n)= f(n-1)+f(n-2). The sequence f(n)mod m is p...
Includes bibliographical references.This paper treats the cycles formed by the residues of different...
In this thesis we are investigating identities regarding Fibonacci sequences. In particular we are e...
In this study, firstly, we analyzed power Fibonacci sequences defined by Ide and Renault in [13]. Th...
In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence r...
An integer sequence (xn)n≥0 is said to be Fibonacci-like if it satisfies the binary recurrence relat...
The Fibonacci sequence can be used as a starting point for an interesting project or research experi...
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
In this paper, we find patterns and count the number of distinct generalised Fibonacci sequences und...
centuries, as it seems there is no end to its many surprising properties. Of particular interest to ...
The purposes of this paper are; (a) to develop a relationship between subscripts of the symbols of F...
The purposes of this paper are; (a) to develop a relationship between subscripts of the symbols of F...
Abstract. The Fibonacci sequence U0 = 1, U1 = 5 and Un = 3 ·Un−1+Un−2 for n ≥ 2 yields a purely peri...
The Fibonacci numbers are defined by the recurrence f(n)= f(n-1)+f(n-2). The sequence f(n)mod m is p...
The Fibonacci numbers are defined by the recurrence f(n)= f(n-1)+f(n-2). The sequence f(n)mod m is p...
Includes bibliographical references.This paper treats the cycles formed by the residues of different...
In this thesis we are investigating identities regarding Fibonacci sequences. In particular we are e...
In this study, firstly, we analyzed power Fibonacci sequences defined by Ide and Renault in [13]. Th...
In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence r...
An integer sequence (xn)n≥0 is said to be Fibonacci-like if it satisfies the binary recurrence relat...
The Fibonacci sequence can be used as a starting point for an interesting project or research experi...
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
We consider the recurrence relation $G_n = G_{n-1} + G_{n-2} + \sum_{j=0}^k \alpha_j n^j$, where $G_...
In this paper, we find patterns and count the number of distinct generalised Fibonacci sequences und...