For those encountering this keyword for the first time, the immediate questions are: Who coined it? What do these numbers represent? And why has internet lore begun to whisper about them?
( L=4 ): ( N=S^4 ) 4 digits. ( S=7 )→2401 sum=7 → works (2+4+0+1=7, 7^4=2401). So 2401 works.
From the left inequality: [ S \ge b^\fracL-1L = b^1 - \frac1L ] From the right inequality: [ S^L \le b^L \implies S \le b ] But ( S ) is an integer digit sum, and maximum digit sum for ( L ) digits in base ( b ) is ( L(b-1) ). However, the inequality ( S^L \le b^L ) is stricter: ( S \le b ).
