[encxhdnj] Base N approximations of pi

For each base, form a sequence of approximations to pi, each one one "digit" longer than the previous.

Base 10: 3, 3.1, 3.14, 3.142, 3.1416, 3.14159, ...

Sort these all of these approximations from worst to best, omitting duplicates.  This involves sorting the concatenation of an infinite list of infinite lists, but it should be possible.

The immediate interesting question is, what is the sequence of bases? 113 will not appear for a very long time.