Given all digits of a sequence S till a certain length say n ie di ( i = 1 to n) ; if the probability of any next block of digits B in next m digits ( m -> infinity ) can be ascertained as < 1/(b^w) where b is the base and w is the string length of the block , through an algorithm which is guaranteed to halt then S is NOT a random sequence.
Just being a normal number is not "sufficient" say the sequence 1234..101102103..10001001 is a normal sequence yet not random.
Based on above since using the spigot formula for Pi I can predict its digits, it is not random.
Direction of analysis is also important. Suppose there is a civilization where constant Pi has not been discovered yet ( let alone its formula), here a only a reverse analysis would be possible and the probability of one chancing upon the spigot formula while analysing the digits of Pi cannot be ruled out though its remote. Other wise the equidistribution of digits would lead such a civilisation to take Pi sequence as random
