Geodesic
...-Expansions, Linear Recurrences, and the Sum-of-Digits Function.
Manuscripta mathematica, Tome 70 (1991) no. 1, pp. 311-324.

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Mots-clés : -expansions, digit expansion of positive integers, real base, sum-of-digits function, asymptotic formula 
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     author = {Robert F. Tichy and Peter J. Grabner},
     title = {...-Expansions, {Linear} {Recurrences,} and the {Sum-of-Digits} {Function.}},
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     year = {1991},
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Robert F. Tichy; Peter J. Grabner. ...-Expansions, Linear Recurrences, and the Sum-of-Digits Function.. Manuscripta mathematica, Tome 70 (1991) no. 1, pp. 311-324. http://geodesic.mathdoc.fr/item/MM2_1991__70_1_155592/