Get the smallest string given a weight (all chars have a weight) - using array

smallestString.cs

//Time: O(n) where n is weight
//Memory: O(1) weights array helper with length . of 26

//In this solution, I am searching in the array of weights from biggest to smallet
//comparing values with weight searched.

//When find a value in the array that fits the weight being searched
//use array index to calculate a char ascii value which represent a
//character wight in the result.

public static string smallestString2(BigInteger weight)
{
    var weigths = new BigInteger[26];
    var startAscii = 65;

    weigths[0] = 1;

    for (int i = 1; i < 26; i++)
    {
        var letterWeight = (i + 1) * weigths[i-1] + weigths[i - 1];
        weigths[i] = letterWeight;
    }

    var sb = new StringBuilder();
    var j = 25;
    while (j >= 0)
    {
        if (weigths[j] <= weight)
        {
            var count = 1;
            while (weigths[j] * count <= weight)
            {
                sb.Insert(0, Convert.ToChar(startAscii + j));
                count++;
            }

            weight -= weigths[j] * (count - 1);
        }

        j--;
    }
    return sb.ToString();
}