Balti Tee 1993 · Ülesanne 3

Solution:

The three consecutive numbers $33 = 3 \cdot 11$, $34 = 2 \cdot 17$ and $35 = 5 \cdot 7$ are all "interesting". On the other hand, among any four consecutive numbers there is one of the form $4k$ which is "interesting" only if $k = 1$. But then we have either $3$ or $5$ among the four numbers, neither of which is "interesting".