User blog comment:Hyp cos/Googolisms hard to extend?/@comment-35470197-20190419220952/@comment-11227630-20190420020121

The post focus on numbers. For "higher-order" objects such as functions, naive extension is allowed.

One way to generally extend FGH + OCF is: let λ be the computable limit of that OCF, and λ[n] be the maximal computable ordinal expressible by the OCF within n symbols; \(f_\lambda(m)\) can extend to \(f_{\lambda2}(m)\), \(f_{\lambda^2}(m)\), \(f_{\lambda^\lambda}(m)\), etc. (using base-λ Wainer hierarchy for ordinals >λ)

The interesting part of 808017424794512875886459904961710757005754368000000000 is the difficulty to find an googological function (or sequence) with it as a term, except the non-special ones such as "f(9) where f(n) = 808017424794512875886459904961710757005754368 × 10^n" which can be generally defined for every number.