Again, what people here are asking is "is pi
". That's the only way that makes sense.
Or to put it a little more precisely, the probability that any given sequence isn't in the first N digits tends to as N tends to infinity
which is not the question at all. After all, the digits of π
are a fixed
string. Suppose I ask "do 20 consecutive 7
's appear in the first 1019
digits of the decimal
expansion of π?" I don't know the answer to this question. But since there is no random
ness involved, the probability
of 20 consecutive 7's appearing in the first 1019
digits of the decimal expansion of π is either 1
(if the answer to the question is "yes
") or 0 (if it's "no
It's best to make the question precise. Either ask if pi is a normal number or ask if every finite sequence of digits appears in the expansion of pi. And the answer to both questions (an affirmative answer to the first would imply an affirmative answer to the second) is unknown.