Integers with a maximal number of Fibonacci representations

Kocábová, Petra; Masáková, Zuzana; Pelantová, Edita

doi:10.1051/ita:2005022

Geodesic

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Integers with a maximal number of Fibonacci representations

Kocábová, Petra ; Masáková, Zuzana ; Pelantová, Edita

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 2, pp. 343-359

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Résumé

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 $F_{k} \leq n < F_{k + 1}$ .

MR Zbl

DOI : 10.1051/ita:2005022

Classification : 11A67, 11B39
Keywords: Fibonacci numbers, Zeckendorf representation

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     title = {Integers with a maximal number of {Fibonacci} representations},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {343--359},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {2},
     year = {2005},
     doi = {10.1051/ita:2005022},
     mrnumber = {2142117},
     zbl = {1074.11008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2005022/}
}

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Kocábová, Petra; Masáková, Zuzana; Pelantová, Edita. Integers with a maximal number of Fibonacci representations. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 2, pp. 343-359. doi: 10.1051/ita:2005022

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