User blog:B1mb0w/Modified Ackermann Function

Hi. I am new to Googology and would like to share my recent thinking.

Modified Ackermann Function The Ackermann function A(x,y) can be modified to increase its growth rate slightly as follows:

MA(x,y) defined as: ◾y+1 if x=0 , ◾MA(x−1,x) if y=0, or ◾A(x−1,A(x,y−1))  otherwise.

I calculate the growth rate to be:

MA(0, y) = y+1 MA(1, y) = y+3 MA(2, y) = 3*y+8 MA(3, y) >> 3^(y+3) MA(4, y) >> 3^^(y+1) MA(5, y) >> 3^^^(y+1) MA(6, y) >> 3^^^^(y+1)

and

MA(x, y) >> 3^^ ... (x-2 arrows) ^^(y+1)