3
$\begingroup$

Possible Duplicate:
Find a closed form for this sequence: $a_{n+1} = a_n + a_n^{-1}$

Suppose $$a_{n+1}=a_n+\frac{1}{a_n}$$ where $a_{1}=1$. Is $f(n)=a_n$ an elementary function?

I haven't found any paper concerning it. Thanks for your attention!

  • 1
    You might be interested in [this paper](http://dx.doi.org/10.1002/jgt.3190190313).2012-08-20
  • 1
    See also http://math.stackexchange.com/questions/63549/generating-functions-and-the-sequence-x-n1-x-n-frac1x-n2012-08-20
  • 0
    @J.M. Thanks a lot!2012-08-20
  • 0
    the elementariness remain unknown2012-08-20
  • 1
    The paper proposed by @J.M. 'The Fractional Chromatic Number Of Mycielski's Graphs' is available at [CiteSeer](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.4280).2012-08-20
  • 0
    References at http://oeis.org/A0738332012-08-20
  • 0
    I know some of the closed form such as $\sqrt{2n+\frac{\log{n}}{2}}$, but I need the elementariness of function $f$, not the upper/lower bound or equivalent infinite2012-08-20

0 Answers 0