User blog comment:B1mb0w/Nested f omega functions/@comment-1605058-20150703155100

Actually, $$f_{\omega+2}^2(3)=f_{\omega+2}(f_{\omega+2}(3))=f_{\omega+1}^{f_{\omega+2}(3)}(f_{\omega+2}(3))$$, not $$f_{\omega}^{f_{\omega+2}(3)}(f_{\omega+2}(3))$$.