Why is this implementation of Superincreasing number sequence not generating an elegant sequence?

class SuperIncreasingNumberSet
{
    List<BigInteger> list;
    //In mathematics, a sequence of positive real numbers 
    //{s_1, s_2, ...} is called superincreasing if every element of 
    //the sequence is greater than the sum of all previous elements 
    //in the sequence.
    public SuperIncreasingNumberSet(BigInteger firstNumber)
    {
        list = new List<BigInteger>();
        list.Add(firstNumber);
    }
    public void Generate(int i)
    {
        BigInteger b = 0;

        for (int j = 0; j < i; j++)
        {
            BigInteger sum = 0;
            foreach(BigInteger bi in list)
            {
                sum = sum + bi;
            }
            Random random = new Random();

            int r = random.Next(1, 5);

            list.Add(sum + r);
        }
    }
    public List<BigInteger> Get()
    {
        return list;
    }
}

class Program
{
    static void Main(string[] args)
    {
        SuperIncreasingNumberSet sins = new SuperIncreasingNumberSet(1);

        sins.Generate(10);

        List<BigInteger> list = sins.Get();

        foreach (BigInteger bi in list)
        {
            Console.Write(bi.ToString()+", ");
        }
    }
}

I was expecting something like this: (1,3,6,13,27,52).

But, mine is generating: (1, 5, 10, 20, 40, 80) and every time it is generating the same sequence.

May be the random isn't working properly.

Why?