Your input happens to be valid Perl syntax, so if you know exactly that your input is in this format (and contains no evil things), you can simply write:

my @array = eval $number;
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Or you could simplify your code a bit:

      for (my $i=$1;$i<=$2;$i++){
        push @arraydigit, $i;
      }
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Can be written shorter and clearer as

     push @array, $1..$2;
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There's really no point in having @array and @arraydigit separate.