More precisely, does there exist an unbounded sequence $a\_0, a\_1, ... \in \mathbb{N}$ of primes such that the function


$\displaystyle O(z) = \sum\_{n \ge 0} a\_n z^n$


is meromorphic on $\mathbb{C}$? 


[A previous version of the question also asked about the exponential generating function of $(a\_n)$. However, such a function can trivially be entire. - GJK]



Does there exist a meromorphic function all of whose Taylor coefficients are prime?
Borel proved the following much stronger result: if a power series with integer coefficients
represents a function f(z) that is meromorphic in a disk of radius >1, then f(z) extends to a rational function on all of C. I found this result without a reference on page 3 of www.mathematik.uni-bielefeld.de/~anugadre/Adeles.pdf.


