User blog comment:King2218/FGH Things/@comment-5029411-20140306005133

f[w]^_{1}n(w) = $$\epsilon$$ = f[w]^f[w]^_{1}n-1(w)(w)

f[w]^_{1}^n(w) = f[w]^_{1}(f[w]^_{1}^n-1(w))(w)

f[w]^_{1}2n(w) = f[w]^_{1}^^_{1}f[w]^_{1}n-1(w)(w)

f[w]^_{2}n(w) = f[w]^_{1}f[w]^_{2}n-1(w)(w)

f[w]^_{3}n(w) = f[w]^_{2}f[w]^_{3}n-1(w)(w)

1. f[0]_0(n)

2. f #_{a+1}(n) = f #^n_{a}(n)

3. f #_{a}(n) = f #_{a[n]}(n)

4. f[x+1]#_0(n) = f[x]_{f[x]_{...}(n)}(n) (n nested) (2nd)

5. f[0]...[0][x+1]#_0(n) = f[0]...[f[0]...[...][x]#_0(n)][x]#_0(n) (n nested) (3rd)

6. f[x]^y #_0(n) = f[x][x]...[x][x] #_0(n) (y x's) (4th)

7. f[x]^zy #_0(n) = f[x]^z-1(f[x]^zy-1 #_0(n)) #_0(n) (5th)