Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.1

A Simpler Normal Number Construction for Simple Lüroth Series

J. Vandehey
University of Georgia at Athens
Department of Mathematics
Athens, GA 30602


Champernowne famously proved that the number 0.(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)... 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.

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Received December 20 2013; revised versions received March 29 2014; April 9 2014. Published in Journal of Integer Sequences, April 15 2014.

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