Friedman numbers

For all who should be studying, working or doing household chores I present some numerical trivia to waste your time lighten your day. Some professor named Erich Friedman came up with the idea of searching for numbers that are equal to a calculation containing the exact same digits that occur in the number. Sounds hard? Not at all. Here are some examples :

126 = 6 × 21
347 = 7³+ 4

Are you starting to get the idea? Named after the inventor they are known as Friedman numbers, but it doesn't stop there. When the digits in the calculation are in the exact same order as in the original number, it's called.... a nice Friedman number. Now isn't that nice. For instance :

1285 = (1 + 2⁸) × 5
2502 = 2 + 50²

It gets even nicer, what do you think of these pandigital (containing all the digits) Friedman numbers :

123456789 = ((86 + 2 × 7)⁵ - 91) ÷34
987654321 = (8 × (97 + 6÷2)⁵ + 1) ÷ 3⁴

These are the only two pandigital ones known, however there's a whole class of repdigit (repeating digits) examples, for instance :

11111111111 = ((11-1)¹¹ - 1 × 1) ÷ (11-1-1)
Or for the diabolically inclined : 6666666666666666 = (6((66-6)÷6)^{6 + (66-6) ÷ 6} - 6) ÷ (6 + (6+6+6)÷6)

It doesn't take a genious to see how ingenious the concept is, however after learning about them I was dying to know if any practical uses have been found. So I sent an email to the inventor :

I recently found out about the notion of Friedman numbers, and I have read the pages about them on Math Magic and Wikipedia. However I was wondering, have there been any practical applications of the concept?

Soon afterwards his reply came