Triples of Consecutive Sphenic Numbers

Theorem
The sequence of triplets of consecutive sphenic numbers starts:
 * $\tuple {1309, 1310, 1311}, \tuple {1885, 1886, 1887}, \tuple {2013, 2014, 2015}, \ldots$

Proof
Note that there cannot be quadruplets of such numbers, since one of the quadruplets must be divisible by $4$, making it non-sphenic.

We have:

hence each number above is sphenic.