Binomial predictors
Number Theory
2009-07-31 v4
Abstract
For a prime p and nonnegative integers n,k, consider the set A_{n,k}^{(p)}={x is in [0,1,...,n]: p^k||binom {n} {x}}. Let the expansion of n+1 in base p be: n+1=alpha_{0} p^{\nu}+alpha_{1}p^{nu-1}+...+alpha_{nu}, where 0<=alpha_{i}<= p-1,i=0,...,nu. Then the number n is called a binomial predictor in base p,if |A_{n,k}^{(p)}|=alpha_{k}p^{nu-k},k=0,1,...,nu. We give a full description of the binomial predictors in base p.
Cite
@article{arxiv.0907.3302,
title = {Binomial predictors},
author = {Vladimir Shevelev},
journal= {arXiv preprint arXiv:0907.3302},
year = {2009}
}
Comments
6 pages; adding a section and new references; generalization on arbitrary prime base