Twist, twist, twist, turn , twist, twist, twist, turn , twist, twist, twist, turn

produces:

0, 1, 2, 3, - \frac{1}{3}, \frac{2}{3}, \frac{5}{3}, \frac{8}{3}, - \frac{3}{8}, \frac{5}{8}, \frac{13}{8}, \frac{21}{8}, - \frac{8}{21}

To return to zero:

if the fraction is negative, then twist (+1);
if the fraction is positive, then turn (-1/x).

twist, turn , twist, twist, turn , twist, twist, twist, turn , twist, twist, twist, turn , twist, twist:
13/21, -21/13, -8/13, 5/13, -13/5, -8/5, -3/5, 2/5, -5/2, -3/2, -1/2, 1/2, -2, -1, 0