On Mon, 25 Jun 2012 18:34:04 +0000 (UTC), Herman Rubin <firstname.lastname@example.org> wrote:
>>> Q: Is it possible to prove the existence of a real number with >>> the property that in order to compute its k-th digit, we must >>> compute all the previous ones? > >> This is not the property of the number, this is property of way >> of computation (algorithm) and also representation of the number.
> For many cases, one need not compute the preceding digits, > but the subsequent ones. [..] > Then using number theory, one could get the contribution > of each term to the desired digit and the subsequent ones, > and hence compute the k-th digit without computing any > previosu ones.
How general is this approach? Can I compute 10th and subsequent decimal digit for Euler number e = sum 1/n!