153 – A Narcissistic Number

mathblab:

153 is a narcissistic number–a number that can be generated from its own digits (so it’s obsessed with itself? hence the narcissism?) like so:

More precisely, a narcissistic number is a natural number that is the sum of its own digits each raised to the power of the number of digits. So since 153 has 3 digits, each digit is cubed and then summed together. There are only four 3-digit 

narcissistic numbers:

A very interesting thing about narcissistic numbers is that, unlike may other sets of numbers (e.g., even/odd numbers, prime numbers, triangular numbers, etc.), there are only finitely many of them. In base 10, there are only 88 (10 of them being the 1 digit numbers). The largest narcissistic number has 39 digits, this guy:

115,132,219,018,763,992,565,095,597,973,971,522,401 

Why is this? Essentially, the sum cannot keep up with the size of the number. More info here: https://en.wikipedia.org/wiki/Narcissistic_number

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