Definition:Tri-Automorphic Number

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.