A Münchhausen number (also called a Munchausen number) is a nonnegative integer equal to the sum of its decimal digits,
each raised to its own power (van Berkel 2009, p. 2;
Kureš 2021, p. 14). It differs from a narcissistic
number, in which each decimal digit is raised to the
common exponent given by the number of digits.
The name refers to the image of Baron von Münchhausen raising himself (van Berkel
2009).
Under the convention used by van Berkel (2009), the only decimal Münchhausen
numbers are 1 and
These are also the only solutions when the digit 0 is excluded. Under the alternative convention , there are exactly four: 0, 1, 3435, and 438579088 (OEIS
A046253).
used by van Berkel (2009), the only decimal Münchhausen
numbers are 1 and
, there are exactly four: 0, 1, 3435, and 438579088 (OEIS
A046253).
