User blog comment:P進大好きbot/BMOCF/@comment-35870936-20181128002342/@comment-35470197-20181128012256

@PsiCubed2

Thank you for the answer :P

@Eclipsed276

See the answer by PsiCubed2. I explicitly write the results.

(Results for \(t = \psi(\psi_{(1,1)}(\psi(0))+\psi_{(1,1)}(0))\)) \begin{eqnarray*} t[0] & = & \psi(\psi_{(1,1)}(\psi(0))) \\ t[1] & = & \psi(\psi_{(1,1)}(\psi(0))+\psi_1(\psi_{(2,1)}(\psi(0)))) \\ t[2] & = & \psi(\psi_{(1,1)}(\psi(0))+\psi_1(\psi_{(2,1)}(\psi(0))+\psi_2(\psi_{(3,1)}(\psi(0))))) \end{eqnarray*}

(Results for \(t = \psi(\psi_{(1,1)}(\psi_1(0))+\psi_{(1,1)}(0))\)) \begin{eqnarray*} t[0] & = & \psi(\psi_{(1,1)}(\psi_1(0))) \\ t[1] & = & \psi(\psi_{(1,1)}(\psi_1(0))+\psi_1(\psi_{(2,1)}(\psi_2(0)))) \\ t[1] & = & \psi(\psi_{(1,1)}(\psi_1(0))+\psi_1(\psi_{(2,1)}(\psi_2(0))+\psi_2(\psi_{(3,1)}(\psi_3(0))))) \end{eqnarray*}