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#Perl, 23 21 bytes

say/^(?!(..+)\1+$)/

using -n option.

Using the regular expression+unary input approach, prints 11 (or whatever number you entered) or a blank line.

Bonus: decimal version, 32 bytes

(1x<>)=~/^1?$|^(11+)\1+$/||say 1

#Perl, 23 20 bytes

say/^(?!(..+)\1+$)/

using -n option.

Using the regular expression+unary input approach, prints 11 (or whatever number you entered) or a blank line.

Bonus: decimal version, 31 bytes

(1x<>)=~/^1$|^(11+)\1+$/||say 1

#Perl, 2321 bytes

say/^(?!(..+)\1+$)/

using -n option

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

#Perl, 23 21 bytes

say/^(?!(..+)\1+$)/

using -n option.

Using the regular expression+unary input approach, prints 11 (or whatever number you entered) or a blank line.

Bonus: decimal version, 32 bytes

(1x<>)=~/^1?$|^(11+)\1+$/||say 1

#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

#Perl, 2321 bytes

say/^(?!(..+)\1+$)/

using -n option

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