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?
For example, the k-th digit of PI can be directly computed without going sequentially through the first k-1. I was wondering what is the general case for algebraic numbers - can their k-th digit be computed ignoring the previous ones? Are there any proves that such a real number exists, or on the contrary - that there can't be such a number? How about other transcendental numbers?