Definition:Perfect Digital Invariant

Definition

Let $n \in \Z_{>0}$ be a positive integer.

$n$ is a perfect digital invariant if and only if when expressed in decimal notation the $n$th powers of its digits add up to some positive integer $m$.

Examples of Perfect Digital Invariants

4150 is a Perfect Digital Invariant to $5$th Powers

$4150 = 4^5 + 1^5 + 5^5 + 0^5$

Also see

• Definition:Recurring Digital Invariant
• Definition:Pluperfect Digital Invariant
• Results about perfect digital invariants can be found here.

Sources

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