  We define a new class of numbers based on the first occurrence of certain
patterns of zeros and ones in the expansion of irracional numbers in a given
basis and call them Sagan numbers, since they were first mentioned, in a
special case, by the North-american astronomer Carl E. Sagan in his
science-fiction novel "Contact." Sagan numbers hold connections with a wealth
of mathematical ideas. We describe some properties of the newly defined numbers
and indicate directions for further amusement.
