Factorial
The factorial numbers are defined with \(0!=1\) and \(n!=n\times(n-1)!\) for \(n\geq1\).
The double factorial numbers are defined with \(0!!=1\), \(1!!=1\) and \(n!!=n\times(n-2)!!\) for \(n\geq2\).
More generally, the \(k\)-factorial numbers are defined with \(0!_{(k)}=1\), \(n!_{(k)}=n\) for \(1\leq n\leq k\), and \(n!_{(k)}=n\times(n-k)!_{(k)}\) for \(n>k\).
Factorial numbers are trivial to factor since they are constructed by multiplying small numbers, but if \(1\) is added or subtracted, then most are hard to factor.
Links
> n! - 1
(table, 0-999)
> n! + 1
(table, 0-999)
> n!! - 1
(table, 0-999)
> n!! + 1
(table, 0-999)
> n!!! - 1
(table, 0-999)
> n!!! + 1
(table, 0-999)
> n!!!! - 1
(table, 0-999)
> n!!!! + 1
(table, 0-999)
> n!!!!! - 1
(table, 0-999)
> n!!!!! + 1
(table, 0-999)