selfnumerical

Selfnumerical refers to a number that is equal to the sum of its own digits, each raised to a power equal to the number of digits in the original number. For example, the number 153 is a selfnumerical because it has three digits, and 1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153. These numbers are also commonly known as Armstrong numbers or narcissistic numbers.

The concept of selfnumerical numbers applies to a specific base, usually base 10 unless otherwise specified. In base 10, the smallest selfnumerical number is 1 (1^1 = 1). Other examples include 370 (3^3 + 7^3 + 0^3 = 27 + 343 + 0 = 370) and 407 (4^3 + 0^3 + 7^3 = 64 + 0 + 343 = 407).

The existence of selfnumerical numbers is a consequence of the interplay between the values of digits and the number of digits. As the number of digits increases, the potential sum of the powered digits also increases rapidly. However, the maximum possible sum of powered digits for an n-digit number grows much slower than the smallest n-digit number itself, which limits the number of selfnumerical numbers for a given base.

While there are infinitely many numbers, the number of selfnumerical numbers is finite for any given base. Finding all selfnumerical numbers for a particular base is a computational task that involves checking each number within a given range.