Geodesic
A simpler normal number construction for simple Lüroth series
Journal of integer sequences, Tome 17 (2014) no. 6.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {17},
     number = {6},
     year = {2014},
     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/