Is the numerical sequence with only one digit, formed by the digits of prime numbers, any less mysterious than the prime number sequence itself? Can it be predicted?

This isn't very clear. Let me try again: 

The primes are  2,3,5,7,11,13,15,...

Your sequence is: 2,3,5,7,1,1,1,3,1,5,...

Is this sequence easier to work with than the primes itself, in terms of predicting primes or deriving a general formula?