A cryptographically secure pseudorandom number generator lets me pump out a stream of digits that's certainly computable, but unless you know my private key, you won't be able to predict it.
(Finding out the private key from the stream is 'computable', because the definition of computable is comfortable with running exponentially long brute force searches. But that's why 'computable' is not a useful definition in practice. You want something that captures 'tractable', not just 'possible on a Turing machine at all'.)
That simple sequence, 1, 10, 100 etc, the digit is at least computable in O(1) time which is maybe a good way to look at predictability. It's a simple rule and no effort similar to computing every digit before it is required.
