Pluperfect Digital Invariant/Examples/3 Digits

Examples of $3$-Digit Pluperfect Digital Invariants

The $3$-digit pluperfect digital invariants are:

$\ds 153$

$=$

$\ds 1 + 125 + 27$

$\ds $

$=$

$\ds 1^3 + 5^3 + 3^3$

$\ds 370$

$=$

$\ds 27 + 343 + 0$

$\ds $

$=$

$\ds 3^3 + 7^3 + 0^3$

$\ds 371$

$=$

$\ds 27 + 343 + 1$

$\ds $

$=$

$\ds 3^3 + 7^3 + 1^3$

$\ds 407$

$=$

$\ds 64 + 0 + 343$

$\ds $

$=$

$\ds 4^3 + 0^3 + 7^3$

Historical Note

In the (some believe inflammatory and controversial) words of G.H. Hardy in his A Mathematician's Apology of $1940$:

These are odd facts, very suitable for puzzle columns and likely to amuse amateurs, but there is nothing in them that appeals to the mathematician. The proofs are neither difficult nor interesting -- merely a little tiresome. The theorems are not serious; and it is plain that one reason ... is the extreme speciality of both the enunciations and the proofs, which are not capable of any significant generalization.

Sources

1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $153$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $153$

Weisstein, Eric W. "Narcissistic Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NarcissisticNumber.html