Perfect digit-to-digit invariant

In number theory, a perfect digit-to-digit invariant (PDDI; also known as a Munchausen number[1]) is a natural number in a given number base that is equal to the sum of its digits each raised to the power of itself. An example in base 10 is 3435, because . The term "Munchausen number" was coined by Dutch mathematician and software engineer Daan van Berkel in 2009,[2] as this evokes the story of Baron Munchausen raising himself up by his own ponytail because each digit is raised to the power of itself.[3][4]

  1. ^ van Berkel, Daan (2009). "On a curious property of 3435". arXiv:0911.3038 [math.HO].
  2. ^ Olry, Regis and Duane E. Haines. "Historical and Literary Roots of Münchhausen Syndromes", from Literature, Neurology, and Neuroscience: Neurological and Psychiatric Disorders, Stanley Finger, Francois Boller, Anne Stiles, eds. Elsevier, 2013. p.136.
  3. ^ Daan van Berkel, On a curious property of 3435.
  4. ^ Parker, Matt (2014). Things to Make and Do in the Fourth Dimension. Penguin UK. p. 28. ISBN 9781846147654. Retrieved 2 May 2015.