Improved Bounds on the Sizes of S.P Numbers
History and Overview
2011-01-04 v2 Number Theory
Abstract
A number which is S.P in base r is a positive integer which is equal to the sum of its base-r digits multiplied by the product of its base-r digits. These numbers have been studied extensively in The Mathematical Gazette. Recently, Shah Ali obtained the first effective bound on the sizes of S.P numbers. Modifying Shah Ali's method, we obtain an improved bound on the number of digits in a base-r S.P number. Our bound is the first sharp bound found for the case r=2.
Keywords
Cite
@article{arxiv.0806.3585,
title = {Improved Bounds on the Sizes of S.P Numbers},
author = {Paul M. Kominers and Scott D. Kominers},
journal= {arXiv preprint arXiv:0806.3585},
year = {2011}
}
Comments
2 pages. To appear, The Mathematical Gazette