Geodesic
Sum-of-digits function for certain non-stationary bases
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 257-267

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We introduce a new approach to the study of sum-of-digits functions for integral non-stationary bases and apply it to certain classical examples, namely to the Cantor and Ostrowski number systems. 
@article{ZNSL_1997_240_a15,
     author = {N. A. Sidorov},
     title = {Sum-of-digits function for certain non-stationary bases},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {257--267},
     publisher = {mathdoc},
     volume = {240},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a15/}
}
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N. A. Sidorov. Sum-of-digits function for certain non-stationary bases. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 257-267. http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a15/