The most famous sequence of numbers in pi is the Feynman Point which comprises the 762nd through 767th decimal places of pi '...999999'. It is named after the physicist Richard Feynman for his remark that he would like to memorise the digits of pi as far as that point; when reciting them, he would be able to finish with '...nine, nine, nine, nine, nine, nine, and so on'.
The Feynman Point is visually very beautiful to me; I see it as a deep, thick rim of dark blue light.
Daniel Tammett, person with synaesthesia and autism, quoted in The Frog Who Croaked Blue by Jamie Ward. Fascinating reading for a current project.
I find Tammett's visualisation incredibly evocative. I suspect this is the test that confirms me as geek.