Pluperfect Digital Invariant/Examples/7 Digits
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Examples of $7$-Digit Pluperfect Digital Invariants
The $7$-digit pluperfect digital invariants are:
| \(\ds 1 \, 741 \, 725\) | \(=\) | \(\ds 1 + 823 \, 543 + 16 \, 384 + 1 + 823 \, 543 + 128 + 78 \, 125\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1^7 + 7^7 + 4^7 + 1^7 + 7^7 + 2^7 + 5^7\) |
| \(\ds 4 \, 210 \, 818\) | \(=\) | \(\ds 16 \, 384 + 128 + 1 + 0 + 2 \, 097 \, 152 + 1 + 2 \, 097 \, 152\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 4^7 + 2^7 + 1^7 + 0^7 + 8^7 + 1^7 + 8^7\) |
| \(\ds 9 \, 800 \, 817\) | \(=\) | \(\ds 4 \, 782 \, 969 + 2 \, 097 \, 152 + 0 + 0 + 2 \, 097 \, 152 + 1 + 823 \, 543\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 9^7 + 8^7 + 0^7 + 0^7 + 8^7 + 1^7 + 7^7\) |
| \(\ds 9 \, 926 \, 315\) | \(=\) | \(\ds 4 \, 782 \, 969 + 4 \, 782 \, 969 + 128 + 279 \, 936 + 2187 + 1 + 78 \, 125\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 9^7 + 9^7 + 2^7 + 6^7 + 3^7 + 1^7 + 5^7\) |
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,741,725$
- Weisstein, Eric W. "Narcissistic Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NarcissisticNumber.html