The pattern is that the nth row from the bottom (starting with n=0) is made by repeating the sequence "0x1x2x...8x9x", where x is a string of 10ⁿ-1 spaces.

use POSIX 'ceil';

sub tape_label {
    my $len = shift() + 1; ## simpler since we'll start at 0  

    my @cols;
    my $n_cols = ceil( log($len) / log(10) );

    for my $log (0 .. $n_cols-1) {
      my $pad     = 10**$log - 1;
      my $pattern = join( " " x $pad, 0 .. 9, "" );

      unshift @cols, substr( $pattern x ceil($len/10**$log), 0, $len )
+;
    }

    return @cols;
}
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But keep in mind, when things get into the thousands, your 1000s digit will only show up every 1000 characters, so it'll be easy to get "lost" on your TM tape.

BTW, I think a "ruler" style marking would be easier to read than a long string of "01234567890123456789" ...

use POSIX 'ceil';

sub tape_label {
    my $len = 5 * ceil(shift() / 5);

    my $l1 = join "", map { sprintf "%-10s", $_*10 } 0 .. ($len/10);
    my $l2 = "|" . ("....|" x ($len/5));

    return "$l1\n$l2\n";
}
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0         10        20        30        40        50        
|....|....|....|....|....|....|....|....|....|....|
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