 Of course, such expansion is not unique in the literal meaning of the word (since "x""s"–1 is not determined uniquely by "x""s"), but all statistical properties of the extended sequence are uniform over its entire length, i.e., are invariant with respect to arbitrary shift (and "x"0 loses its meaning of an "initial" condition).The sequence "X" is equivalent to a sequence of integers "K" = (..., "k"−1, "k"0, "k"1, "k"2, ...), constructed by the rule "k""s" = [1/"x""s"–1].Inversely, every number of X is determined by the integers of K as an infinite continuous fraction

(the convenience of introducing the notation formula_84 with an index shifted by 1 will become clear in the following).