NARCISSISTIC NUMBERS

Narcissistic numbers are positive integers that can be expressed as the sum of their own digits raised to a power equal to the number of digits in the number. In other words, a narcissistic number is a number that is equal to the sum of its own digits raised to the power of the number of digits.

Examples of narcissistic numbers

1. 153 = 1^3 + 5^3 + 3^3
2. 370 = 3^3 + 7^3 + 0^3
3. 407 = 4^3 + 0^3 + 7^3

Properties of narcissistic numbers

1. _Symmetry_: Narcissistic numbers have an interesting symmetry, since they can be expressed as the sum of their own digits raised to a power equal to the number of digits.
2. _Rarity_: Narcissistic numbers are relatively rare, since not all positive integers can be expressed in this way.
3. _Diversity_: Narcissistic numbers can have any number of digits, which makes them interesting to study.

Types of narcissistic numbers

1. _Narcissistic base 10 numbers_: These are the narcissistic numbers that are expressed in base 10, like the previous examples.
2. _Narcissistic base n numbers_: These are the narcissistic numbers that are expressed in base n, where n is a positive integer other than 10.

Algorithm to find narcissistic numbers

1. _Start a loop_: Start a loop that iterates over all positive integers.
2. _Calculate the sum_: Calculate the sum of the digits of the number raised to the power of the number of digits.
3. _Check equality_: Check if the sum is equal to the original number.
4. _Print the result_: If the sum is equal to the original number, print the number as a narcissistic number.

I hope this information has been useful to you. If you have any more questions, don't hesitate to ask!