What are Munchausen Numbers?

Answer 1

A Munchhausen number is an integer which is equal to the sum of each of its digits raised the power of that digit.

There are only 2 proper Munchhausen numbers and these are

1 = 1^1

and

3435 = 3^3 + 4^4 + 3^3 + 5^5.

0^0 is not a well-defined number: 0^n = 0 for all positive n (undefined for negative n), and k^0 = 1 for all non-zero k, then is 0^0 = 0 or 1?

If you accept that 0^0 = 0 then there are two more Munchhausen numbers: 0 and 438579088.

The numbers are called Munchhausen numbers because they raise themselves to their own power - in a way reminiscent of Baron Hieronymus von Munchhausen in the 1943 comedy film - who elevated himself by riding a cannonball.

The numbers are also called Munchausen numbers (single h).