Add to ORKGA beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers {Fn}∞n=1. Lekkerkerker proved that the average number of summands for integers in [Fn, Fn+1) is n/(ϕ 2+1), with ϕ the golden mean. This has been generalized to the following: given nonnegative integers c1, c2,..., cL with c1, cL> 0 and recursive sequenc
ABSTRACT. Zeckendorf proved any integer can be decomposed uniquely as a sum of non-adjacent Fibonacc...
The sequence of Fibonacci numbers is given by 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 6...
This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: give...
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum of non-...
AbstractA beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum...
ABSTRACT. Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum o...
Abstract. Zeckendorf proved that every positive integer has a unique representation as a sum of non-...
Abstract A beautiful theorem of Zeckendorf states that every integer can be writ-ten uniquely as a s...
ABSTRACT. Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum o...
Let (Fn)n=1∞ be the classical Fibonacci sequence. It is well known that the limFn+1/Fn exists and eq...
Abstract. Zeckendorf’s theorem states that every positive integer can be uniquely decom-posed as a s...
ABSTRACT. By Zeckendorf’s theorem, an equivalent definition of the Fibonacci sequence (appro-priatel...
Abstract. An interesting characterization of the Fibonacci numbers is that, if we write them as F1 =...
These notes put on record part of the contents of a conversation the first author had with John Conw...
Abstract. An interesting characterization of the Fibonacci numbers is that, if we write them as F1 =...
ABSTRACT. Zeckendorf proved any integer can be decomposed uniquely as a sum of non-adjacent Fibonacc...
The sequence of Fibonacci numbers is given by 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 6...
This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: give...
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum of non-...
AbstractA beautiful theorem of Zeckendorf states that every integer can be written uniquely as a sum...
ABSTRACT. Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum o...
Abstract. Zeckendorf proved that every positive integer has a unique representation as a sum of non-...
Abstract A beautiful theorem of Zeckendorf states that every integer can be writ-ten uniquely as a s...
ABSTRACT. Zeckendorf’s theorem states that every positive integer can be written uniquely as a sum o...
Let (Fn)n=1∞ be the classical Fibonacci sequence. It is well known that the limFn+1/Fn exists and eq...
Abstract. Zeckendorf’s theorem states that every positive integer can be uniquely decom-posed as a s...
ABSTRACT. By Zeckendorf’s theorem, an equivalent definition of the Fibonacci sequence (appro-priatel...
Abstract. An interesting characterization of the Fibonacci numbers is that, if we write them as F1 =...
These notes put on record part of the contents of a conversation the first author had with John Conw...
Abstract. An interesting characterization of the Fibonacci numbers is that, if we write them as F1 =...
ABSTRACT. Zeckendorf proved any integer can be decomposed uniquely as a sum of non-adjacent Fibonacc...
The sequence of Fibonacci numbers is given by 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 6...
This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: give...