To play the "fraction game" corresponding to a given list f1, f2, ..., fk of fractions and starting integer N, you repeatedly multiply the integer you have at any stage (initially N) by the earliest fi in the list for which the answer is integral. Whenever there is no such fi, the game stops.
Formally, we define a sequence by S0=N, and Sj+1=fiSj, if for 1<=i<=k, the number fiSj is an integer but the numbers f1Sj, ..., fi-1Sj are not.
For example, if we have the list of eight fractions f1=170/39, f2=19/13, f3=13/17, f4=69/95, f5=19/23, f6=1/19, f7=13/7, f8=1/3, and start with N=21, we produce the (finite) sequence (21,39,170,130,190,138,114,6,2). In general, the sequence may be infinite.Given a fraction list and a starting integer calculate a part of the defined sequence. Actually, we are interested only in the powers of 2 that appear in the sequence.