For normality, see <https://en.wikipedia.org/wiki/Normal_number>. For random number/sequence, see <https://en.wikipedia.org/wiki/Algorithmically_random_sequence>.


Now, is there any number that is normal in every bases $b > 1$ except random numbers (or numbers expansion of which is algorithmically random sequence)?


I suspect, there is only normal number in some bases except random number, normality in every bases $b>1$ is a strong requirement to exclude computable numbers normal in some bases. In other word, is it possible that normality in every bases $b>1$ is contradicted theoretically?


Because computability of numbers is contradict to randomness. Normality in every bases $b>1$ may leads the number to be random one. So another question is: Could Normality in every bases $b>1$ pass the randomness test?



Existence of normal number except random numbers
Computable, absolutely normal numbers do actually exist. See 


V. Becher, S. Figueira: *[An example of a computable absolutely normal number](https://doi.org/10.1016/S0304-3975(01)00170-0)*, Theoretical Computer Science **270** (2002), 947-958. 


