Generating shuffled range using a PRNG rather than shuffling

Question

Is there any known algorithm that can generate a shuffled range [0..n) in linear time and constant space (when output produced iteratively), given an arbitrary seed value?

Answer 1

Based on Jason's answer, I've made a simple straightforward implementation in C#. Find the next largest power of two greater than N. This makes it trivial to generate a and c, since c needs to be relatively prime (meaning it can't be divisible by 2, aka odd), and (a-1) needs to be divisible by 2, and (a-1) needs to be divisible by 4. Statistically, it should take 1-2 congruences to generate the next number (since 2N >= M >= N).

class Program
{
    IEnumerable GenerateSequence(int N)
    {
        Random r = new Random();
        int M = NextLargestPowerOfTwo(N);
        int c = r.Next(M / 2) * 2 + 1; // make c any odd number between 0 and M
        int a = r.Next(M / 4) * 4 + 1; // M = 2^m, so make (a-1) divisible by all prime factors, and 4

        int start = r.Next(M);
        int x = start;
        do
        {
            x = (a * x + c) % M;
            if (x < N)
                yield return x;
        } while (x != start);
    }

    int NextLargestPowerOfTwo(int n)
    {
        n |= (n >> 1);
        n |= (n >> 2);
        n |= (n >> 4);
        n |= (n >> 8);
        n |= (n >> 16);
        return (n + 1);
    }

    static void Main(string[] args)
    {
        Program p = new Program();
        foreach (int n in p.GenerateSequence(1000))
        {
            Console.WriteLine(n);
        }

        Console.ReadKey();
    }
}