So here's a bet:
I give you the 10^100th digit of the above algorithm and you give me the 10^100th digit of pi.
Whoever fails owes the other side 10 BTC.
I give you the 10^100th digit of the above algorithm and you give me the 10^100th digit of pi.
Whoever fails owes the other side 10 BTC.
Describe the n-th digit of an irrational number without calculating all previous positions of the number.
If pi were a sequence of digits, there is no algorithm to calculate it other than by calculating pi but there is one for op's number. The very fact that he could show the algorithm for creating the sequence of numbers in his post is indicative of that.
For pi such an algorithm doesn't exist (other than calculating pi itself).
I wanted to emphasize this by talking about the "sequence of digits" in my original reply but apparently I failed at explaining this well.
Maybe I should rephrase it:
My assumption is: If there is an O(1) algorithm to determine the n-th digit of an irrational number x then the number is still "of a different class" than the likes of pi and there OP might not be able to induce things from this "lesser class of irrational numbers"
However, it's just an intuition