I have a function $F(x)$ which can be calculated as following:
$$ f(1) = x $$ $$ f(n) = f(n - 1) + \lfloor\frac{ f(n-1) - 1 }{ f(1) - n + 1 }\rfloor, \text{ } \text{ } n>1 $$ $$ F(x) = f(x) $$
We need to find $F(N)$ for any value of $N\geqslant1$
This recurrence function could've been easily manipulated into a generic formula for the $N$th term if it wasn't for the greatest integer function. However, due to its presence I'm utterly confused on how to proceed. Any help would be appreciated.