User blog comment:Simply Beautiful Art/A finite variant to the Madore's OCF./@comment-31663462-20171214231130

Let $$M(n)=\max(C'(n))$$ and $$\psi'(n)=k+1$$. By writing numbers in the form of $$\sum_{i=0}^{M(n)}\gamma_i,\gamma_i\le k$$, we get the lower bound of $$\psi'(n+1)>kM(n)$$, and since $$M(n+1)=M(n)^{M(n)+1}$$, we get tetrational growth. Better bounds may be found, and if $$\psi'(3)=71$$, then we have the lower bound of $$\psi'(4)>18790477090$$.