#Perl, 23 bytes
say<>=~/^(?!(..+)\1+$)/
Using the regular expression+unary input approach, prints 11 (or whatever your digit entered) or a blank line
Bonus: decimal version, 32 bytes
(1x<>)=~/^1?$|^(11+)\1+$/||say 1
ThaddeusB
- 401
- 2
- 8