Sequence of Smallest 3 Consecutive Triangular Numbers which are Sphenic

Theorem
The smallest $3$ consecutive triangular numbers which are sphenic is:
 * $406$, $435$, $465$

Proof
Let $T_n$ denote the $n$th triangular number.

The smallest sphenic number is $30$.

Hence we need investigate triangular number from where $T_n \ge 30$.

Thus:

Also see

 * There exist no 4 Consecutive Triangular Numbers which are all Sphenic Numbers