Base 2
Patterns that can be factored: \[[1^*01^*_2]_n=2\cdot2^{2n}-2^{n}-1=\left(2^{n}-1\right)\left(2\cdot2^{n}+1\right)=\left([1^*_2]_n\right)\left([10^*1_2]_n\right)\]
Links
> 10001: Depression 100..001
(table)
> 10111: Near Repdigit 1011..11
(table)
> 11101: Near Repdigit 11..1101
(table)
> 11111: Repunit 11..11
(table)