A Münchhausen number (sometimes spelled Münchausen number, with a single 'h') is a number equal to the sum of its digits raised to each digit's power. Münchhausen
numbers therefore differ from narcissistic numbers,
which are numbers that equal the sum of a fixed power (in particular, the number
of decimal digits) of the given number. The name "Münchhausen number"
derives from the fact that these numbers "raise themselves" analogously
to way in which Baron Hieronymus von Münchhausen allegedly raised himself by
riding a cannonball, as portrayed in the 1943 fantasy comedy film Münchhausen.
If 0s are disallowed (since is not well-defined), the only Münchhausen numbers
are 1 and
If the definition
is adopted, then there are exactly four Münchhausen numbers: 0, 1, 3435, and
438579088 (OEIS A046253).
is not well-defined), the only Münchhausen numbers
are 1 and
is adopted, then there are exactly four Münchhausen numbers: 0, 1, 3435, and
438579088 (OEIS A046253).
