Knuth's conjecture writing integers "using only one 4"

[Maximilian Hasler]

Indeed one finds your page when googling Knuth's title, but I did notnotice the updated information.(Did the humble webmaster achieve the forthcoming paper with the proof ?)However, on scanning the page anew, I only now discovered the reference to"A Note on N!" by John E. Maxfield, 1970.This seems to refer to existence (resp. density) and not minimality(which is my main concern), but I'll check it out in detail.(Remark: concerning existence, there is no difference between 4 and 9since they can be expressed in terms of each other. Also it should benoted that 3 is in some sense the most natural choice in the sense itis the smallest possible choice for which the problem makes sense.)
Thanks,MaximilianPS: the four 4's or four 9's or four π games seem less related to theprecise question posed here (minimal number of two unary operationsneeded for n, starting always from the same given number).Another related problem, in the sense of minimality of therepresentation, would be the recently discussed notion of integercomplexity.