Compositorial
Let \(c_n\) be the \(n\)th composite, so \(c_1=4,c_2=6,c_3=8,c_4=9,\ldots\). The \(n\)th compositorial number is \(c_n!/c_n\#=c_1c_2\ldots c_n\) where \(\#\) means primorial.
These numbers are products of many small numbers and easy to factor, but adding or subtracting 1 makes most hard to factor.