Perfect digit-to-digit invariant

In number theory, a perfect digit-to-digit invariant (PDDI; also known as a Munchausen number) is a natural number in a given number base b {\displaystyle b} that is equal to the sum of its digits each raised to the power of itself. An example in base 10 is 3435, because 3435 = 3 3 + 4 4 + 3 3 + 5 5 {\displaystyle 3435=3^{3}+4^{4}+3^{3}+5^{5}} .