Sequence of 4 Consecutive Square-Free Triplets

Theorem
The following sets of $4$ consecutive triplets of integers, with one integer between each triplet, are square-free:


 * $29, 30, 31; 33, 34, 35; 37, 38, 39; 41, 42, 43$


 * $101, 102, 103; 105, 106, 107; 109, 110, 111; 113, 114, 115$

Proof
Note that $32, 36, 40$ and $104, 108, 112$ are all divisible by $4 = 2^2$, so are by definition not square-free.

Then inspecting each number in turn:

Also see

 * Sequence of Square-Free Triplets