Improved Bounds on the Sizes of S.P Numbers

Details Improved Bounds on the Sizes of S.P Numbers Improved Bounds on the Sizes of S.P Numbers

2008-06-23

arxiv.org/abs/0806.3585v2

Note 94.05, The Mathematical Gazette 94(529), (2010), 127-129

Mathematics

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2 pages. To appear, The Mathematical Gazette

Scientific paper

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.

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