Vital reading is chapter 17 of "At Play With J", by Eugene McDonnell
 http://www.jsoftware.com/jwiki/At%20Play%20With%20J

Here's my resultant page of notes made back in 2010. Touches on the
points in this thread:

See: Contact, by Carl Sagan, for a novel pivoting heavily on finding
patterns in pi.

Piphilology comprises the creation and use of mnemonic techniques to
remember a span of digits of the mathematical constant π. The word is
a play on Pi itself and the linguistic field of philology.

The Indiana Pi Bill, an 1897 attempt by the Indiana state legislature
to dictate a solution to the unending decimal problem by legislative
fiat.

Pi search...
http://www.angio.net/pi/piquery
http://en.wikipedia.org/wiki/String_searching_algorithm
Probability of finding strings in pi http://www.angio.net/pi/whynotpi.html

Should the search for meaningful sequences in pi be called perimancy?

The Feynman Point: APWJ p136
http://www.jsoftware.com/jwiki/Doc/Articles/Play151

From end of Eugene McDonnell's article:
"Before we part, let’s look at a consecutive portion of these digits:
   (762+i.6){q1000
999999
Hmmm. Well, yes, that’s not too unusual.* In fact, if such strings
didn’t occur every now and then, it would argue against randomness."

FOOTNOTE: * Eugene has selected the so-called Feynman Point, a
six-digit sequence 999999 in the decimal expansion of π to which
Richard Feynman (1918-1988) used to draw attention in his lectures to
make an instructive joke about what is and what is not perceived as
random. (Ed.)
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