The first human player to use e.g. "md5(3891*seq) odd", wins. You can quibble over how long it should take to describe how a sequence is encoded into a bitstring, but even sets where every sequence is of length 1 can be infinite.

Or heck, how about just the binary representation of pi? You don't even need any functions beyond basic arithmetic (eg. if all the famous constants are well known, just pick the decimal expansion of some suitable rational).