Abstract
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.
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Funding
This work was financially supported by the Russian Science Foundation, project 19-11-00065, https://rscf.ru/en/project/19-11-00065/.
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Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 447–457 https://doi.org/10.4213/mzm13609.
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Shutov, A.V. On the Sum of Digits of Expansions of a Pair of Consecutive Numbers over a Linear Recurrent Sequence. Math Notes 114, 387–396 (2023). https://doi.org/10.1134/S0001434623090092
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DOI: https://doi.org/10.1134/S0001434623090092