Definition:Tri-Automorphic Number
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Definition
A tri-automorphic number is a positive integer $n$ such that $3 n^2$ ends in a repetition of $n$.
Sequence of Tri-Automorphic Numbers
The sequence of tri-automorphic numbers begins:
- $2, 5, 7, 67, 75, 92, 667, 792, 875, 6667, 6875, 9792, \ldots$
Examples
$6667$ is Tri-Automorphic
| \(\ds 3 \times 6667^2\) | \(=\) | \(\ds 3 \times 44 \, 448 \, 889\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 133 \, 34 \mathbf {6 \, 667}\) |
Also see
- Results about tri-automorphic numbers can be found here.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6667$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6667$