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): $153$