Geodesic
On one sum associated with Fibonacci numeration system
Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 2, pp. 271-275

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We obtain the asymptotic formula for the sum $S(X)=\sum_{n$, 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. 
@article{DVMG_2020_20_2_a15,
     author = {A. V. Shutov},
     title = {On one sum associated with {Fibonacci} numeration system},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {271--275},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2020_20_2_a15/}
}
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A. V. Shutov. On one sum associated with Fibonacci numeration system. Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 2, pp. 271-275. http://geodesic.mathdoc.fr/item/DVMG_2020_20_2_a15/