Wednesday, July 16, 2025

Narcissistic Numbers

 (Image: Narciso (Jan Cossiers), CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons)

In Greek mythology, Narcissus was known for his beauty. He rejected advances from all suitors, both men and women, and instead fell in love with his own reflection. The legend gives us the source of the words narcissist and narcissistic. 

There are also numbers known as Narcissistic Numbers. In the On-Line Encyclopedia of Integer Sequences (OEIS), sequence A005188 defines such numbers to be:  m-digit positive numbers equal to the sum of the m-th powers of their digits.

For example, the number 153 has 3 digits. The sum of 1^3 + 5^3 + 3^3 = 153. The sequence of Narcissistic Numbers begins: 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407...

Narcissistic Numbers.

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