Possible Comment on A007095

N. J. A. Sloane njas at research.att.com
Mon May 21 22:59:11 CEST 2007

The latest issue (May 2007) of The College Mathematics Journal has a "Classroom Capsule" that generalizes this result.
"On the Convergence of Some Modified p-Series" by Dongling Deng


From: Jeremy Gardiner [mailto:jeremy.gardiner at btinternet.com] 
Sent: Monday, May 21, 2007 2:49 AM
To: sequence fans
Subject: Possible Comment on A007095

Dear seqfans,

I saw the following at Jeremy Rouse's maths problems web page:


Problem 10.  Let S be the set of positive integers that, when written in base 10, does not contain the digit 9. Show that the sum of 1/n over all n * S converges and is less than 80. (Problem 157, USSR Olympiad Problem Book). 

This could make an interesting comment on A007095 (Numbers in base 9, also numbers without 9 as a digit), but can anyone confirm the reference?

My guess from a google search is this may be from "The USSR Olympiad Problem Book : Selected Problems and Theorems of Elementary Mathematics" by D. O. Shklarsky, N. N. Chentzov, and I. M. Yaglom (Paperback - Sep 28 1993), however I do not possess a copy.

Jeremy Gardiner

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