Geodesic
On the Sum of Digits of Expansions of a Pair of Consecutive Numbers over a Linear Recurrent Sequence
Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 447-457

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We obtain asymptotic formulas for the number of positive integers $n\le X$ such that the sums of digits of the expansions of $n$ and $n+1$ over some linear recurrent sequences have a given parity.
Keywords: linear recurrent sequence, greedy expansion, sum of digits. 
@article{MZM_2023_114_3_a8,
     author = {A. V. Shutov},
     title = {On the {Sum} of {Digits} of {Expansions} of a {Pair} of {Consecutive} {Numbers} over a {Linear} {Recurrent} {Sequence}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {447--457},
     publisher = {mathdoc},
     volume = {114},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a8/}
}
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A. V. Shutov. On the Sum of Digits of Expansions of a Pair of Consecutive Numbers over a Linear Recurrent Sequence. Matematičeskie zametki, Tome 114 (2023) no. 3, pp. 447-457. http://geodesic.mathdoc.fr/item/MZM_2023_114_3_a8/