A narcissistic number (also called an Armstrong number or plus-perfect number) equals the sum of its own digits each raised to the power of the digit count.
The canonical example is 153: it has 3 digits, and \(1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153\).
The narcissistic numbers in base 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, …
There are only 88 narcissistic numbers in base 10 — proven by D. Winter in 1985. The largest has 39 digits. Beyond that, no \(n\)-digit number can equal the sum of \(n\)-th powers of its digits because the maximum possible sum grows too slowly.