Almost Integer

[Ed Pegg Jr]

I recently did a column on this topic.
http://www.maa.org/editorial/mathgames/mathgames_03_15_05.html

I think my favorite item here is the fourth root of 9.1, which
is subtly related to 
http://www.research.att.com/projects/OEIS?Anum=A002072 -- I was
dismissive of 9.1 at first, but NJA liked it. He wound up
being correct that it was related to another sequence.

Ed Pegg Jr.

Dean Hickerson wrote:
> Yasutoshi Kohmoto wrote:
> 
> 
>>Recently Mathworld's description about "Almost Integer" was updated.
>>I expected my example which I had mailed to Eric Weisstein was described
>>on it.
>>         Pi^14/(9103887*Zeta(9))=1.00000000004539
>>But he didn't do so.
>>
>>    Is it not interesting?
> 
> 
> Not very.  Suppose you compute all numbers of the form
> 
>     pi^ab / (cdefghi * zeta(j))
> 
> where a,b,...,j are decimal digits.  There are 8999999100 choices for the
> digits, so it's not surprising that one of them has 10 zeroes after the
> decimal point.  If you found one that had a lot more than 10 zeroes, that
> might be interesting.  (E.g., pi^8/(9450 * zeta(8)) = 1.000000000000..., but
> here we already know that it's exactly 1.)
> 
> Another way to write your equation is:  pi^14/zeta(9) = 9103887.0004132...
> There are 900 choices for the digits in  pi^ab/zeta(c),  so again it's not
> surprising that there's one with 3 zeroes after the decimal point.
> 
> Dean Hickerson
> dean at math.ucdavis.edu