Another googologic function, the y sequence.
The notation was by Yukito, a japanese googologist.
Y(1,2) = Y(1,1,1,1,1,1,1,1,1,1,...)
Y(1,2,2) = Y(1,2,1,2,1,2,1,2,...)
Y(1,2,2,2) = Y(1,2,2,1,2,2,1,2,2,...)
...
Y(1,2,3) = Y(1,2,2,2,2,2,2,2,...)
Y(1,2,3,3) = Y(1,2,3,2,3,2,3,2,3,...)
...
Y(1,2,4) = Y(1,2,3,4,5,6,7,8,9,10,11,...) [Limit of PrSS], Epsilon-zero
Y(1,2,4,1) = Y(1,2,4) Epsilon-zero + 1
Y(1,2,4,2) = Y(1,2,4,1,2,4,1,2,4,...)
Y(1,2,4,3) = Y(1,2,4,2,4,2,4,2,...)
Y(1,2,4,4) = Y(1,2,4,3,5,4,6,5,7,6,8,7,9,8,10,9,11,10,12,11,13,12,14,13,15,14,16,15,17,16,18,17,19,18,20,19,21,20,22,21,...)
Y(1,2,4,5) = Y(1,2,4,4,4,4,...) φ(ε0,0) ?
Y(1,2,4,6) = Y(1,2,4,5,7,8,10,11,13,14,...) Γ0 ?
Y(1,2,4,7) = Y(1,2,4,6,8,10,12,14,16,...) ψ(ε_(Ω+1)) = ψ(Ω_2)
Y(1,2,4,8)= Y(1,2,4,7,11,16,21,27,...) (basically the difference goes up by one every time, starting from 1 at 1) [Limit of PSS], ψ(Ω_ω)
Y(1,3) = Y(1,2,4,8,16,32,64,...) [Limit of BMS]
Y(1,4) = Y(1,3,9,27,81,243,729,2187,...)
Y(1,5) = Y(1,4,16,64,256,1024,4096,...)
Y(1,ω) LIMIT OF Y-SEQUENCE AND 2-D BMS