# Possible Comment on A007095

Max Alekseyev maxale at gmail.com
Mon May 21 22:03:47 CEST 2007

```On 5/21/07, Max Alekseyev <maxale at gmail.com> wrote:

> >  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.
>
> The original russian version of this book is freely available at:
> http://ilib.mccme.ru/djvu/bib-mat-kr/shk-1.htm (vol. 1: number theory)
> http://ilib.mccme.ru/djvu/bib-mat-kr/shk-2.htm (vol. 2: planimetry)
> http://ilib.mccme.ru/djvu/bib-mat-kr/shk-3.htm (vol. 3: stereometry)
>
> But the problem 157 there has nothing to do with the problem mentioned above.

Heh. Jeremy, your reference is correct. To check that out just go to
search 157 inside the book, and click onto Page 36 in the search results.

So, English translation is somewhat different from Russian original.

Max

Jeremy, i think the [sequence of decimal digits of the]
number is in the OEIS.
Neil

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.

As I recall, Bob Wilson (rgwv) was involved in
computing it, or extending it. - Bob?

Neil

Straightforward duplicates:

A106734 and A106752
A085587 and A085594
A108916 and A108940
A087844 and A087848
A089134 and A089135
A094572 and A098357 (after adjusting for offsets)
A123335 and A123361 (after adjusting for offsets)
A069742 and A069743

Possible duplicates:

A108198 and A128717
http://www.research.att.com/~njas/sequences/?q=id:A108198|id:A128717

A105143 and A105164
http://www.research.att.com/~njas/sequences/?q=id:A105143|id:A105164

A002548 and A093763 (after adjusting for offset diffs)
http://www.research.att.com/~njas/sequences/?q=id:A002548|id:A093763

A095149 and A124326
http://www.research.att.com/~njas/sequences/?q=id:A095149|id:A124326

A066016 and A098068 (if A066016 is also full)
http://www.research.att.com/~njas/sequences/?q=id:A066016|id:A098068

```