Donald Knuth’s up-arrow notation is based on the fact that multiplication can be viewed as iterated addition and exponentiation as iterated multiplication. A single arrow just represents exponentiation. Multiple arrows means iterating the operation associated with one less arrow. So if you have 2 arrows, that’s iterated exponentiation, or tetration. If you have 3 arrows, that’s iterated tetration, or pentation. So on and so forth.

The general definition of the notation is as follows: Knuth Notation

Because I love recursion and the definition uses recursion (and because reddit’s Daily Programmer Challenge #365 told me to), I decided to give this a shot in C#. It’s actually really easy to do in a few lines of code.

/* Knuth's Up Arrow Notaion */
static double up(double a, double b, double n)
    if (n == 1) return Math.Pow(a, b);
    else if (n>=1&&b==0)return 1;
    else return up(a, up(a, (b-1), n), n-1);