# Possible Comment on A007095

Nick Hobson nickh at qbyte.org
Tue May 22 13:55:43 CEST 2007

```Jeremy,

This is an example of a Kempner series; see
http://www.qbyte.org/puzzles/p072s.html#kempner for some approximate sums,
and a reference to "Gamma: Exploring Euler's Constant", by Julian Havil.

Nick

On Mon, 21 May 2007 07:48:39 +0100, Jeremy Gardiner
<jeremy.gardiner at btinternet.com> wrote:

> Dear seqfans,
>
> I saw the following at Jeremy Rouse's maths problems web page:
>
> http://www.math.wisc.edu/~rouse/problems.html
>
> 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
>

Zak,   the conventions have changed over the years.  This entry

%I A040112
%S A040112
2,3,7,19,29,31,37,47,59,83,103,109,113,131,139,167
%N A040112 x^4 = 7 has a solution mod p.
%K A040112 nonn
%O A040112 0,1
%A A040112 njas

%I A040112
%S A040112 2,3,7,19,29,31,37,47,59,83,103,109,113,131,139,167,193,199,223,227,
%T A040112 251,271,283,307,311,367,383,389,419,439,449,457,467,479,503,523,563,
%U A040112 587,607,613,619,643,647,653,691
%N A040112 Primes p such that x^4 = 7 has a solution mod p.
%Y A040112 Adjacent sequences: A040109 A040110 A040111 this_sequence A040113 A040114 A040115
%Y A040112 Sequence in context: A073641 A078373 A038878 this_sequence A074855 A038935 A073640
%K A040112 nonn
%O A040112 1,1
%A A040112 njas

- better name, better offset

The trouble is, I have 10,000 things to do
and nor enough time

Neil

Seqfans,  I heard this work on the radio
last night.  I've never heard a musical
piece which so closely resembles an integer sequence!
Does anyone have the score?
Neil

```