The Maximal Order of Hyper-($b$-ary)-expansions

Michael Coons, Lukas Spiegelhofer

Abstract


Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-($b$-ary)-expansions of a nonnegative integer $n$ for general integral bases $b\geqslant 2$.


Keywords


Stern's diatomic sequence, Hyper base expansions, Maximal order

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