And the three most common operators.

I'd say the four most common operators: Addition, multiplication, exponentiation, and test-for-equality. :-)

Those three operators are the first three hyper operators. 1st (Addition), 2nd (Multiplication) and 3rd (Exponentiation).

I wonder if throwing in the 4th hyper operator, tetration, and the value phi produces anything.

Thanks for introducing me to tetration; I had never heard of that before.

http://en.wikipedia.org/wiki/Tetration