[pndmnm]

In fact, it's still not known if pi is normal (contains all finite patterns of numbers[π]), so you can't guarantee that any search will terminate.

π: Not quite the definition of normal, but equivalent.

[calvins]

Even if pi isn't normal, there are plenty of normal numbers to choose from (almost all of the reals are normal, in fact), including some really simple and predictable ones like Champernowne's constant (in base 10: 0.1234567891011121314...) that would support simpler index calculations than pi.