User blog comment:Emlightened/Competition - Nov 2018/@comment-27513631-20181107231112/@comment-27513631-20181108222151

\(f_n\) is defined for any \(n \in \mathbb N \cup \{\infty\}\) (where \(\forall n\in \mathbb N. n < \infty\)).

The definition reduces to:

\(C_\infty(0) = \{0,1\}\)

\(C_\infty(k+1) = \{a+b, f_b(a) | a,b \in C_\infty(k)\}\)

\(f_\infty(k) = \max\;C_\infty(k)\)