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I'm aware that there are a lot BBP type formulas out there which extract the n-th digit of the observed constant.

I'm asking for the reverse action, namely, is it possible to find the first occurrence of a given digit (or string of digits) within a constant? If not, any related work, analysis and other hints are welcome.

user3209815
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    Have fun with http://www.angio.net/pi/piquery.html. Search for your birthday and read "How the Pi-Searcher Works" in that page. – Claude Leibovici Jul 06 '14 at 08:25
  • If you came up with a formula for it you would be famous... at least on math.stackexchange :) You should do it! :) – Neil Mar 21 '15 at 05:22

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In short, there is no good way to determine the first occurrence of a string of digits within $\pi$. In fact, we do not know whether every finite string of digits actually occurs in $\pi$. [We believe this is true, but we do not know how to show it].

For some particular constants, it's rather easy. For instance, perhaps the simplest normal number is the number $0.12345678910111213\ldots$, formed by concatenating all base $10$ digits together. It should be pretty easy to determine the first occurrence of a string of digits here, but this is a very contrived example.

davidlowryduda
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