Let us call an integer n > 2 strong if the greatest prime divisor of n is greater than the greatest prime divisor of (n + 1). Then, obviously, every odd prime is a strong number, but there are also many composite strong numbers, the smallest of which is 14. (Whether the fact that 14 is the smallest strong number is related to the fact that the answer to Kuratowski’s closure-complement problem is 14 would itself be an interesting question.)
So, have what I am calling strong numbers already been given a name, and, in any case is there a pattern to them?