Cubic Recurring Digital Invariant/Examples/160

Example of Cubic Recurring Digital Invariant

$160$ is a cubic recurring digital invariant:

\(\ds 160: \ \ \)

\(\ds 1^3 + 6^3 + 0^3\)

\(=\)

\(\ds 1 + 216 + 0\)

\(\ds = 217\)

\(\ds 217: \ \ \)

\(\ds 2^3 + 1^3 + 7^3\)

\(=\)

\(\ds 8 + 1 + 343\)

\(\ds = 352\)

\(\ds 352: \ \ \)

\(\ds 3^3 + 5^3 + 2^3\)

\(=\)

\(\ds 27 + 125 + 8\)

\(\ds = 160\)

$\blacksquare$

Proof

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