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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - A. V. Shutov
TI  - On one sum associated with Fibonacci numeration system
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2020
SP  - 271
EP  - 275
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2020_20_2_a15/
LA  - ru
ID  - DVMG_2020_20_2_a15
ER  - 
%0 Journal Article
%A A. V. Shutov
%T On one sum associated with Fibonacci numeration system
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2020
%P 271-275
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2020_20_2_a15/
%G ru
%F DVMG_2020_20_2_a15
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/

[1] K. Mahler, “The Spectrum of an Array and its Application to the Study of the Translation Properties of a Simple Class of Arithmetical Functions: Part Two On the Translation Properties of a Simple Class of Arithmetical Functions”, J. Math. and Physics, 6 (1927), 158–163 | DOI | Zbl

[2] A. Shutov, “On sum of digits of the Zeckendorf representations of two consecutive numbers”, Fibonacci Quarterly, 58:3 (2020), 203–207 | MR

[3] E. Zeckendorf, “Representation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas”, Bull. Soc. R. Sci. Liege, 41 (1972), 179–182 | MR | Zbl

[4] E. P. Davletyarova, A. A. Zhukova, A. V. Shutov, “Geometrizatsiya sistemy schisleniya Fibonachchi i ee prilozheniya k teorii chisel”, Algebra i analiz, 25:6 (2013), 1–23 | MR

[5] V. G. Zhuravlev, “Odnomernye razbieniya Fibonachchi”, Izv. RAN. Ser. matem., 71:2 (2007), 89-–122 | MR | Zbl

[6] K. M. Eminyan, “Ob odnoi binarnoi zadache”, Matematicheskie zametki, 60:4 (1996), 478-481 | MR | Zbl