A family of digit functions with large periods
Number Theory
2012-10-23 v3
Abstract
For odd n>=3, we consider a general hypothetical identity for the differences S_{n,0}(x) of multiples of n with even and odd digit sums in the base n-1 in interval [0,x), which we prove in the cases n=3 and n=5 and empirically confirm for some other n. We give a verification algorithm for this identity for any odd n. The hypothetical identity allows to give a general recursion for S_{n,0}(x) for every integer x depending on the residue of x modulo p(n)=2n(n-1)^{n-1}, such that p(3)=24, p(5)=2560, p(7)=653184, etc.
Keywords
Cite
@article{arxiv.1209.5705,
title = {A family of digit functions with large periods},
author = {Vladimir Shevelev and Peter J. C. Moses},
journal= {arXiv preprint arXiv:1209.5705},
year = {2012}
}
Comments
15 pages Two new sections