A Spigot Function is one that indexes the individual digits from an infinitely long number in at least one base.

Two specific numbers for which spigot functions have been found are Pi, e, and the Cx Champernowne's Constants in various bases especially C2 and C10. In some cases it may be efficient to retrieve numeric strings from Intangible Memory in computers specialized for experimental or recreational mathematics. It is known to me that if C10 is multiplied by a googolplex, then the decimal point will fall between a 5 and a 6. To be able to know something about a number that would not be inside this universe if it were full of that number is a thrilling, especially numbers that by definition contains the complete predicted set of all digital information. C2 is specifically the set of all binary data and would be more useful.

I will update with the Spigot Functions for Pi, C2, C10 and others when I locate them in my notebooks. For Cx, there are each three interesting and simple functions:

Find a specific number in Cx and return a pointer to it.
Given a pointer, retrieve a digit.
"Guess" the beginning of the number pointed to.

(Guessing only fails if the pointer is on a number that is found with a shorter than expected pointer, in which case "rewinding" the pointer is trivial.

For pi, the spigot function seems to prefer power of 2 bases for instant retrieval of any digit, but may take a long time to convert to Base 10. In alphaBase 26, Pi=C.NOIZE___ but when played as a WAV file it sounds like the hissing noise of a tube-TV with no channel to watch. The Cx numbers are more (but certainly not less) musical sounding.

A silly example spigot function for 1/7 may be:
d=714285/(10^(5-(p modulo 6))modulo 10)
which should give the pth digit of .142857142857142857_
basically making d=the remainder+1th digit of 142857, from p/6

spigot functions for Pi and e

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