  Let s_k/t_k, k>= 0, be the convergents of the continued fraction expansion of
a real number x. We investigate the sequence of Jacobi symbols (s_k/t_k), k>=
0. We show that this sequence is purely periodic with shortest possible period
length 24 for x=e=2.718281... and shortest possible period length 40 for x=e^2.
Further, we make the first steps towards a general theory of such sequences of
Jacobi symbols. For instance, we show that there are uncountably many numbers x
such that this sequence has the period 1 (of length 1), and that every natural
number L actually occurs as the shortest possible period length of some x.
