# sum of 1/A007504(n)

Don Reble djr at nk.ca
Mon May 21 18:44:48 CEST 2007

```Seqfans:

I might as well do this bit.

Summing n=4016708412 primes, I get p(n)=97434417233,
primeSum=191462469311735988657,
seriesSum=1.02347632390000000000618+.
Anyone want to double-check?

And I compute an upper bound of 1.02347632395-.

--
Don Reble  djr at nk.ca

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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 =
=91
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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<HTML>
<TITLE>Possible Comment on A007095</TITLE>
<BODY>
<FONT FACE=3D"Arial">Dear seqfans,<BR>
<BR>
I saw the following at Jeremy Rouse's maths problems web page:<BR>
<BR>
<FONT COLOR=3D"#0000FF"><U>http://www.math.wisc.edu/~rouse/problems.html</U=
></FONT> <BR>
<BR>
Problem 10.  Let <I>S</I> be the set of positive integers that, when w=
ritten in base 10, does not contain the digit 9. Show that the sum of <I>1/=
n</I> over all <I>n </I></FONT><I><FONT FACE=3D"Symbol">=91</FONT><FONT FAC=
E=3D"Arial"> S</FONT></I><FONT FACE=3D"Arial"> converges and is less than 8=
0. (Problem 157, USSR Olympiad Problem Book). <BR>
<BR>
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?<BR>
<BR>
My guess from a google search is this may be from "The USSR Olympiad P=
roblem Book : Selected Problems and Theorems of Elementary Mathematics&quot=
; by D. O. Shklarsky, N. N. Chentzov, and I. M. Yaglom (Paperback - Sep 28 =
1993), however I do not possess a copy.<BR>
<BR>
Jeremy Gardiner<BR>
</FONT>
</BODY>
</HTML>

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```