Section: A. Introduction D. Numbers that pwn 2-digit 3-digit 4-digit ... < 2000 4-digit ... < 4000 E. Code / Algorithm # Pretty Wild Narcissistic Numbers– numbers that pwn

Dr Colin Rose

Comparison Table
 Ordered Concatenation Operators Example Reference Vampire Numbers  only products 1435 = 35 × 411827 = 21 × 87 ¤ Vampires¤ MathWorld Friedman Numbers  +   –   ×   ÷   ^ 126 = 21 × 6289 = (8+9)2 ¤ Erich Friedman ¤ Sloane A036057 Wild Narcissistic  anything 1448 = 1!×4 + c(4) + c(8)c(n) = nth Catalan number ¤ Mike Keith Pretty Wild Narcissistic - numbers that pwn  +   –   ×   ÷   ^and ! 729 = 1704 = (1+70)4!

Notes:
1. Armstrong numbers (Sloane A005188), also known as pluperfect digital invariants, are m-digit numbers n equal to the sum of the mth powers of their digits. Here is a 3-digit example:
407 = 43 + 03 + 73
They are neither wild nor pretty because they require the use of the the power term m (the 3 in this example) over and above the digits of integer n (or, alternatively, the use of more than one copy of each digit of n) to achieve a solution. They are sometimes known as m-narcissistic numbers. However, the use of the term 'narcissistic' to describe them seems more confusing than it is helpful.

2. The subset of Friedman numbers that are ordered are pretty wild. Ordered Friedman numbers are known as 'nice' Friedman numbers (see Sloane A080035).