User blog comment:Maxywaxy/Someone tell me if this is right/@comment-35470197-20181109033603

Your description of \(f_3\) is wrong.

It can be computed in the following way: \begin{eqnarray*} f_3(0) & = & 0 \\ f_3(1) & = & f_2(1) \\ & = & 1 * 2^1 \\ f_3(2) & = & f_2(f_2(2)) \\ & = & 2 * 2^2 * 2^{2 * 2^2} \\ f_3(3) & = & f_2(f_2(f_2(3))) \\ & = & 3 * 2^3 * 2^{3 * 2^3} * 2^{3 * 2^3 * 2^{3 * 2^3}} \\ f_3(4) & = & f_2(f_2(f_2(f_2(4)))) \\ & = & 4 * 2^4 * 2^{4 * 2^4} * 2^{4 * 2^4 * 2^{4 * 2^4}} * 2^{4 * 2^4 * 2^{4 * 2^4} * 2^{4 * 2^4 * 2^{4 * 2^4}}} \end{eqnarray*} Namely, repeat \(f_2(n)\) \(n\)-times.