User blog comment:Lord Aspect/SATCLN IV/@comment-31966679-20180713031604

A[n] = f_w(n)

A1[n] = f_w + 1(n)

A2[n] = f_w + 2(n)

An[n] = f_w2(n)

AAn[n] = f_w2 + 1(n)

AAAn[n] = f_w2 + 2(n)

A...(n As)...An[n] = f_w3(n)

Un[n] = f_w3(n)

UUn[n] = f_w4(n)

UUUn[n] = f_w5(n)

U...(n Us)...Un[n] = f_w ^ 2 + 2(n)

Гn[n] = f_w ^ 2 + 2(n)

So your number, Г(10 ^^^ 100)[9] would be roughly f_{w ^ 2 + 2}(10 ^^^ 100)