343

The number 343 is a self generating number. Starting with the digits of the original number, you can re-generate it by adding common mathematical symbols.

343 = ( 3 + 4 ) ^ 3
        =( 7 ) ^ 3
        = 7 x 7 x 7
        =( 7 x 7 ) x 7
        =( 49 ) x 7
        =343 Q.E.D.

This came to me in a flash of inspiration one day when I was parking in a hotel garage with numbered spaces. I noticed an empty space up ahead. When I got closer, I saw it was space 343 and the rest just popped into my mind.

I posted this to a newsgroup and got a few other self-generating numbers from Kristal, these using factorials.

1! + 4! + 5! = 1 + (1 X 2 X 3 X 4) + (1 X 2 X 3 X 4 X 5)
                   = 1 + 24 + 120
                   = 145

AND

(-(1-4))!x4! = (-(-3))! X 4!
                   =3! X 4!
                   = (1 X 2 X 3) X (1 X 2 X 3 X 4 )
                   = 6 X 24
                   = 144

Here's one from Dolphinius. exp(x) is the function e ^ x, where e is the base of natural logarithms, an irrational number approximately 2.7182818. If you plug the numbers into an Excel spreadsheet, it works out exactly.

exp { (2+1) X ln(6) } = exp(3 X 1.791759469)
                                  = exp(5.375278408)
                                  = 216

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