How to convert a base 10-number to 3-base in net (Special case)

I'm looking for a routine in C# that gives me the following output when putting in numbers: 0 - A 1 - B 2 - C 3 - AA 4 - AB 5 - AC 6 - BA 7 - BB 8 - BC 9 - CA 10 - CB 11 - CC 12 - AAA 13 - etc

I'm using letters, so that it's not so confusing with zero's. I've seen other routines, but they will give me BA for the value of 3 and not AA.

Note: The other routines I found was Quickest way to convert a base 10 number to any base in .NET? and http://www.drdobbs.com/architecture-and-design/convert-from-long-to-any-number-base-in/228701167, but as I said, they would give me not exactly what I was looking for.

Solution

Converting between systems is basic programming task and logic doesn't differ from other systems (such as hexadecimal or binary). Please, find below code:

//here you choose what number should be used to convert, you wanted 3, so I assigned this value here
int systemNumber = 3;
//pick number to convert (you can feed text box value here)
int numberToParse = 5;
// Note below
numberToParse++;
string convertedNumber = "";
List<char> letters = new List<char>{ 'A', 'B', 'C' };
//basic algorithm for converting numbers between systems
while(numberToParse > 0)
{
    // Note below
    numberToParse--;
    convertedNumber = letters[numberToParse % systemNumber] + convertedNumber;
    //append corresponding letter to our "number"
    numberToParse = (int)Math.Floor((decimal)numberToParse / systemNumber);
}
//show converted number
MessageBox.Show(convertedNumber);

NOTE: I didn't read carefully at first and got it wrong. I added to previous solution two lines marked with "Note below": incrementation and decrementation of parsed number. Decrementation enables A (which is zero, thus omitted at the beginning of numbers) to be treated as relevent leading digit. But this way, numbers that can be converted are shifted and begin with 1. To compensate that, we need to increment our number at the beginning.

Additionaly, if you want to use other systems like that, you have to expand list with letter. Now we have A, B and C, because you wanted system based on 3. In fact, you can always use full alphabet:

List<char> letters = new List<char> {'A','B','C', 'D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z'};

and only change systemNumber.