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.
Key words:Fibonacci numeration system, sum of digits.