User blog comment:P進大好きbot/Cheatsheet on Properties of OCFs/@comment-28606698-20191202084133

According to system for FS on the site page you refer to, the sequence α[n] for α=ψ_0(ψ_{ω+1}(0)+ψ_1(0)) should be:

α[0]=ψ_0(ψ_{ω+1}(0)+ψ_0(0)),

because

ψ_0(ψ_{ω+1}(0)+ψ_1(0))[0]= ψ_0((ψ_{ω+1}(0)+ψ_0(0))[ ψ_0(0)]) due to rule 7, and

(ψ_{ω+1}(0)+ψ_0(0))[ ψ_0(0)]= ψ_{ω+1}(0)+(ψ_1(0)[ ψ_0(0)]) = ψ_{ω+1}(0)+ ψ_0(0) due to rules 1 and 3,

further

α[1]=ψ_0(ψ_{ω+1}(0)+ψ_0(ψ_{ω+1}(0)+ψ_0(0))),

α[2]=ψ_0(ψ_{ω+1}(0)+ψ_0(ψ_{ω+1}(0)+ψ_0(ψ_{ω+1}(0)+ψ_0(0)))),

…

i.e. ω+1 instead ω.