$hash->{$i} = printf("$line %d",$_);

This line seems so wrong to me. printf prints something to STDOUT, and returns 1 on success. So this will basically store 1 in $hash->{$i}. Also the hash keys are always numerical - why use a hash at all? An array seems much more appropriate, and easier to handle.

    print OUT $hash->{3};# . "\n";
    print OUT $hash->{4};# . "\n";
    print OUT $hash->{5};# . "\n";
    print OUT $hash->{6};# . "\n";
    print OUT $hash->{7};# . "\n";
    print OUT $hash->{8};# . "\n";
    print OUT $hash->{9};# . "\n";
    #print  $hash->{1} . "1<br>";
    print  $hash->{2} . "2<br>";
    print  $hash->{3} . "3<br>";
    print  $hash->{4} . "4<br>";
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Programming is mostly having the computer do the boring repetitions for you. No need for something like this, you have loops in Perl.

When I read in the text line by line, I can check for the 014 shift out ASCII character however when I use the print OUT $line the ASCII character is wrong.

If you don't tell me what "wrong" means to you I can't help you.

The output does contain a 014 character, but if you view it in a browser I guess you don't see it. hexdump is very well suited to inspect the output.