Let's pretend that all digits of pi are known and arbitrarily long sequences of digits are trivial to get. Further, some mathematician proves that there are no patterns in pi. We could create a stream cipher by grabbing a piece of pi as long as our plaintext and combining the two with some function (such as XOR or modulus addition.) The key would be the starting position in pi.
Would this be equivalent (in terms of security) to a one-time pad? To what sort of attacks would it be vulnerable?