*Narcissus, as drawn by Oliver Herford from "An alphabet of celebrities," 1899.In this drawing, Narcissus is admiring a daffodil, formally known as a Narcissus.Every time I hear the word, "vanity," I think of the 1972 song, "You're So Vain," by Carly Simon.(Portion of a Wikimedia Commons image from Project Gutenberg)*

Physicists and mathematicians enjoy giving things unusual names. In physics, we have elementary particles with

This is a finite sequence of just 88 elements, the last of which being153 = 1^{3}+ 5^{3}+ 3^{3}

8208 = 8^{4}+ 2^{4}+ 0^{4}+ 8^{4}

4210818 = 4^{7}+ 2^{7}+ 1^{7}+ 0^{7}+ 8^{7}+ 1^{7}+ 8^{7}

*Computation time for Armstrong numbers on a personal computer having a dual core 3600 MHz Intel i3-4160 64-bit Linux computer with 8 gigabytes of memory.My Raspberry Pi Model 4B is a factor of 3.6 times slower.(Graphed using Gnumeric. Click for larger image.)*

If we look beyond our ten-finger mindset, we see that Armstrong numbers exist in other number bases, such as base-8 (octal). The number,

A related sequence, if you're willing to call two numbers a sequence, are the Münchausen numbers, which are the two numbers equal to the sum of their digits raised to the digit's power. These numbers, named after a character in a 1943 film, are 1 and 3435,[4-5]660_{8}= 6^{3}+ 6^{3}+ 0^{3}

If we allow zero to the power of zero to be equal to zero, 01 = 1^{1}

3435 = 3^{3}+ 4^{4}+3^{3}+5^{5}= 27 + 256 + 27 + 3125

*An Armstrong of a different kind.Edwin Armstrong (1890-1954) was the inventor of FM radio and the superheterodyne radio receiver.Significant inventions are often coveted by others, as the history of Alexander Graham Bell's telephone and the laser has shown. Armstrong's FM radio principle was coveted by RCA, which gave him no end of troubles, and this was apparently one cause of Armstrong's suicide.Armstrong was one of the most prolific and influential inventors in radio, having more than fifty patents in his name.(Armstrong, circa 1954, in a Wikimedia Commons image.)*

- Armstrong (or pluperfect, or Plus Perfect, or narcissistic) numbers (A005188), The On-Line Encyclopedia of Integer Sequences.
- Eric W. Weisstein, "Narcissistic Number," From MathWorld--A Wolfram Web Resource.
- Program for Armstrong Numbers - GeeksforGeeks.
- A variant of Munchausen numbers (A046253), The On-Line Encyclopedia of Integer Sequences.
- Eric W. Weisstein, "Münchhausen Number," From MathWorld--A Wolfram Web Resource
- Henk Koppelaar and Peyman Nasehpour, "On Hardy's Apology Numbers," arXiv, August 18, 2020.