User blog comment:PsiCubed2/Letter Notation Part III/@comment-30118230-20161226190930/@comment-30754445-20161226194315

You're right about P10 = (10,12 (1) 2) rather than what I wrote. I'll fix it in a moment.

As for you question: every letter has both an unary form and a binary form. So both mJn and Jn are valid expressions. In fact, Jx (for any positive real x) was defined first:

Jx = (1,0)|x

while xJn was defined only later as:

xJn = J(n+log₅(x/2))

So:

3K3 = JJJ3 = J(J(J3)) = (1,0)|(1,0)|(1,0)|3.