http://public.logica.com/~stepneys/cyc/a/ackermnn.htm
http://public.logica.com/~stepneys/cyc/b/big.htm
http://www.lifesmith.com/mathfun.html
http://home.earthlink.net/~mrob/pub/largenum.html
definition
A(0, n) = n + 1
A(m+1, 0) = A(m, 1)
A(m+1, n+1) = A(m, A(m+1, n))
relations
A(0, n) = n + 1
A(1, n) = 2 + (n + 3) - 3 = n + 2
A(2, n) = 2 x (n + 3) - 3 = 2*n+3
A(3, n) = 2 ^ (n + 3) - 3
A(4, n) = 2 ^^ (n + 3) - 3
....
where "+" is defined as a+b = 1+(a+(b-1))
where "*" is defined as a*b = a+(a*(b-1))
where "^" is defined as a^b = a*(a^(b-1))
where "^^" is defined as a^^b = a^(a^^(b-1))
OP(n,a,b)= OP(n-1,a,OP(n,a,b-1))
OP(0,a,b)=1+b OP(1,a,b)=a+b OP(2,a,b)=a*b OP(3,a,b)=a^b
A(m,n)=OP(m,2,n+3)-3