### Far Eastern Mathematical Journal

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On one sum associated with Fibonacci numeration system

Shutov A.V.

2020, issue 2, Ñ. 271–275
DOI: https://doi.org/10.47910/FEMJ202028

Abstract
We obtain the asymptotic formula for the sum $S(X)=\sum_{n<X}\varepsilon(n)\varepsilon(n+1)$, where $\varepsilon(n)$ takes the value $+1$ or $-1$ depending on the parity of the expansion of the sum of the digits $n$ in the Fibonacci numeration system.

Keywords:
Fibonacci numeration system, sum of digits