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Topic: One Through Nine, With Eight Missing, And Two Ones
Replies: 19   Last Post: Mar 31, 2011 5:11 PM

 Messages: [ Previous | Next ]
 Dan Hoey Posts: 172 Registered: 12/6/04
Re: One Through Nine, With Eight Missing, And Two Ones
Posted: Mar 30, 2011 4:48 PM

On 3/29/11 10:25 PM, James Van Buskirk wrote:
> "Dan Hoey"<haoyuep@aol.com> wrote in message
> news:imu38o\$o5d\$1@speranza.aioe.org...
>

>> On 3/25/2011 12:25 AM, James Van Buskirk wrote:
>>> Given the O.P. I was hoping for something like the sum of the
>>> reciprocals of all the positive integers that don't have the digit
>>> '8'.

>
>> I like this more than Leroy Quet's puzzle. Do you have any ideas
>> about how to calculate this number?

>
> I calculated up to double or quadruple precision once. The version
> with 9 as the missing digit was from the Olympiad problem book and
> you can start with the proof that the series converges and apply
> a little more effort and get to something you can evaluate. No one
> has ever given an independent calculation that I can check against,
> however.

According to http://oeis.org/A082837, the sum of reciprocals of
positive integers that don't have the digit 8 is
22.726365402679370602833644156742557889210702616360219843536376162.
For those without the digit 9, http://oeis.org/A082838 has
22.920676619264150348163657094375931914944762436998481568541998356.
Robert Baillie has a paper at http://arxiv.org/abs/0806.4410v2 that
covers these and related topics and includes Mathematica code.

Dan

Date Subject Author
3/24/11 Leroy Quet
3/24/11 Leroy Quet
3/24/11 Ilan Mayer
3/24/11 Dan Hoey
3/24/11 Leroy Quet
3/24/11 Dan Hoey
3/25/11 Leroy Quet
3/26/11 Leroy Quet
3/28/11 Leroy Quet
3/28/11 quasi