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Integers with a maximal number of Fibonacci representations

Petra Kocábová, Zuzana Masáková, Edita Pelantová (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study the properties of the function R ( n ) which determines the number of representations of an integer n as a sum of distinct Fibonacci numbers F k . We determine the maximum and mean values of R ( n ) for F k n < F k + 1 .

Integers with a maximal number of Fibonacci representations

Petra Kocábová, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

We study the properties of the function R(n) which determines the number of representations of an integer n as a sum of distinct Fibonacci numbers Fk. We determine the maximum and mean values of R(n) for Fk ≤ n < Fk+1.

Iterated digit sums, recursions and primality

Larry Ericksen (2006)

Acta Mathematica Universitatis Ostraviensis

We examine the congruences and iterate the digit sums of integer sequences. We generate recursive number sequences from triple and quintuple product identities. And we use second order recursions to determine the primality of special number systems.

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