Fractions involving the number of different ways a number can be expressed as a sum of powers of 2.
Define f(0)=1 and f(n
) to be the number of ways to write n
as a sum of powers of 2 where no power occurs more than twice.
For example, f(10)=5 since there are five different ways to express 10:
10 = 8+2 = 8+1+1 = 4+4+2 = 4+2+2+1+1 = 4+4+1+1
It can be shown that for every fraction p/q
0) there exists at least one integer n
For instance, the smallest n
for which f(n
-1)=13/17 is 241.
The binary expansion of 241 is 11110001.
Reading this binary number from the most significant bit to the least
significant bit there are 4 one's, 3 zeroes and 1 one. We shall call the
string 4,3,1 the Shortened Binary Expansion
Find the Shortened Binary Expansion of the smallest n
Give your answer as comma separated integers, without any whitespaces.