>> the only operators being add and multiply; no factorials
>> The expression is elegant in its economy.
>I reckon some kind of factorial, say of the largest prime >factor of the given number, with all the 2's and maybe some >other stuff divided out might do it.
No, no, no!
Given what is above (and I have snipped away all the subtler clues, leaving only the blatant ones), your answer is, well, quite ludicrous. :-)
111 PI J(n):J(1)=1,J(k+1)=10*J(k)+1 n=1
or, if you prefer
REP(3) PI REP(n) n=REP(1)
Please see my reply to Bill Hart, who got half way there.
Intuition and induction are important in mathematical creativity. Virgil, I suggest you spend time pondering the (base-independent) shapes of naturals, which will enhance your enjoyment and comfort in your search for beauty and truth.