Münchhausen Numbers

 

(Image: Statue of Baron Münchhausen riding half of a horse - https://commons.wikimedia.org/wiki/User:Franzfoto)

Baron Münchhausen is a fictional character known for making exaggerated stories (other spellings include Munchhausen and Munchausen). In addition to the fables of the Baron, the name is used to describe Münchhausen syndrome and Münchhausen syndrome by proxy, in which someone fabricates a story of their illness or the illness of one they care for to gain attention or sympathy.

There are also numbers known as Münchhausen Numbers. These are numbers that equal the sum of each of their digits raised to their own power. For example, in base ten, the numbers include 1 and 3435. 1^1=1, 3^3 +4^4+3^3+5^5=3435. This sequence of numbers is A046253 in the On-Line Encyclopedia of Integer Sequences (OEIS). Another sequence of other Münchhausen Numbers is A166623, which lists such numbers in multiple bases.