it is rather trivial to calculate F(N) for each integer value of M 1 to 2016, after doing that and sorting by F(N) (I used 1.60934 as my conversion factor M to N) I get the two smallest values for M = 1349 and 878
For M=1349, N=2170.99966 and F(N)=0.00034
for M=878, N=1413.00052 and F(N)=0.00052
Based on the definition of F(N), F(N) has a theoretical min of 0 and max of 0.5. Min happening when N is an integer and max when fractional part of N is 0.5
Within the given constraints, M=1788 gets really close to the theoretical max with N=2877.49992

Posted by Daniel
on 20160226 09:50:52 