User blog comment:SuperSpruce/Question about certain fundamental sequences/@comment-32213734-20190422053122

I'll try to answer using Scorcher007's list of ordinals and my program Ordinal Explorer v4.0, but I'm not sure, since I do not know "ψ OCFs" very well.

I think that ψ((Ω_ω)+Ω_2) is #452 in Scorcher007's list, and in my program it may be [M][M]M = [[Ω2]Ωω] = [Ωω + Ω2]

Fundamental sequence, generated by my program (with presumptive correspondence to "ψ OCF"):
 * ][[]M = [[]Ωω] = [Ωω + ω] = ψ(Ωω + ω)
 * [[][[]M[M]]]M = [[[Ωω + ω]Ω]Ωω] = ψ(Ωω + ψ1(Ωω + ω))
 * [[[[][[]M[M]]]M[M]]]M = ψ(Ωω + ψ1(Ωω + ψ1(Ωω + ω)))
 * [[[[[[][[]M[M]]]M[M]]]M[M]]]M = ψ(Ωω + ψ1(Ωω + ψ1(Ωω + ψ1(Ωω + ω))))
 * [[[[[[[[][[]M[M]]]M[M]]]M[M]]]M[M]]]M = ψ(Ωω + ψ1(Ωω + ψ1(Ωω + ψ1(Ωω + ψ1(Ωω + ω)))))
 * [[[[[[[[[[][[]M[M]]]M[M]]]M[M]]]M[M]]]M[M]]]M = ψ(Ωω + ψ1(Ωω + ψ1(Ωω + ψ1(Ωω + ψ1(Ωω + ψ1(Ωω + ω))))))

ψ(ψΙ(Ω)) may be #629 in Scorcher007's list, and [[M]&M]M]M = [[[[M]&#93;[I]M]I] = [[M + I + Ω]I] in my program.

Fundamental sequence:
 * [][[[M]MM]M]M = [[[][I]M]I] = [[M + I + ω]I] = ψ(ψI(ω))
 * [[[[][[[M]MM]M]M][M]MM]M]M = ψ(ψI(ψ(ψI(ω))))
 * [[[[[[[][[[M]MM]M]M][M]MM]M]M][M]MM]M]M = ψ(ψI(ψ(ψI(ψ(ψI(ω))))))
 * [[[[[[[[[[][[[M]MM]M]M][M]MM]M]M][M]MM]M]M][M]MM]M]M = ψ(ψI(ψ(ψI(ψ(ψI(ψ(ψI(ω))))))))
 * [[[[[[[[[[[[[][[[M]MM]M]M][M]MM]M]M][M]MM]M]M][M]MM]M]M][M]MM]M]M = ψ(ψI(ψ(ψI(ψ(ψI(ψ(ψI(ψ(ψI(ω))))))))))
 * [[[[[[[[[[[[[[[[][[[M]MM]M]M][M]MM]M]M][M]MM]M]M][M]MM]M]M][M]MM]M]M][M]MM]M]M = ψ(ψI(ψ(ψI(ψ(ψI(ψ(ψI(ψ(ψI(ψ(ψI(ω))))))))))))