User blog comment:Nedherman1/New Notation Idea/@comment-35470197-20180713222712

There is no definition of \(f_1(n)\), if you regard the suffix \(a\) of \(f_a(n)\) is just the alphabet \(a\). (And \(f_n(n)\) is critically ambiguous when \(n\) is the alphabet \(n\).)