Geodesic
A simpler normal number construction for simple Lüroth series
Journal of integer sequences, Tome 17 (2014) no. 6
Champernowne famously proved that the number $0.(1)(2)(3)$(4)$(5)(6)(7)$(8)$(9)(10)(11)(12)\dots $formed by concatenating all the integers one after another is normal to base 10. We give a generalization of Champernowne's construction to various other digit systems, including generalized Lüroth series with a finite number of digits. For these systems, our construction simplifies a recent construction given by Madritsch and Mance. Along the way we give an estimation of the sum of multinomial coefficients above a tilted hyperplane in Pascal's simplex, which may be of general interest.
Classification : 11K16
Keywords: normal number, multinomial coefficient 
@article{JIS_2014__17_6_a6,
     author = {Vandehey,  J.},
     title = {A simpler normal number construction for simple {L\"uroth} series},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {6},
     zbl = {1294.11124},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_6_a6/}
}
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Vandehey,  J. A simpler normal number construction for simple Lüroth series. Journal of integer sequences, Tome 17 (2014) no. 6. http://geodesic.mathdoc.fr/item/JIS_2014__17_6_a6/