Basically you're looking for a small integral relation among the powers of the given number. This can be done effectively with the LLL algorithm (Lenstra-Lenstra-Lovasz) and variations of it (especially PSLQ), and indeed this approach is used to determine "inverse symbolic" candidates for an approximate real number. Look up papers by Plouffe and Bailey such as [this one][1]. 


  [1]: http://www.google.com/url?sa=t&source=web&ct=res&cd=4&ved=0CBYQFjAD&url=http%3A%2F%2Fcrd.lbl.gov%2F~dhbailey%2Fdhbpapers%2Fpslq-cse.pdf&ei=Mj3nSp-zCpjYtAPXi_ybAQ&usg=AFQjCNGnae-chOA_Wdif1Tmhs4BwvX3sSA&sig2=vor2JXGPKLko3BBxRZXiwQ