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

\(\displaystyle 3 \times 6667^2\) \(=\) \(\displaystyle 3 \times 44 \, 448 \, 889\)
\(\displaystyle \) \(=\) \(\displaystyle 133 \, 34 \mathbf {6 \, 667}\)


Also see

  • Results about tri-automorphic numbers can be found here.


Sources