Context: I found a function that simulates the results from throwing an $N$-sided die. That is, a function $f(N,n)$ composed of elementary functions and the floor or ceiling function such that the numbers $f(N,1), f(N,2), f(N,3), ...$ are a pseudorandom sequence of integers ranging from $1$ to $N$:
$f(N,n)=\lceil\frac{N}{\pi}\arccos{(\cos{(10^n)})}\rceil$
Here is a plot of $f(6,n)$ against $n$:
Now I am wondering, is there a function that produces pseudorandom permutations of the first $N$ positive integers? That is, a function $g(N,n)$ composed of elementary functions and the floor or ceiling function such that, for $k\in\mathbb{N}$ , the numbers $g(N,kN+1), g(N,kN+2), g(N,kN+3), ..., g(N,kN+N)$ are a pseudorandom permutation of the first $N$ positive integers.
I do not know how to make the function's outputs not repeat within each interval of $N$ outputs.