my @line_nums = (44, 87, 345);

my $line_num = shift(@line_nums);
my $more = 2;

while (<>) {
   next if $. != $line_num;

   print;

   if ($more) {
      --$more;
      ++$line_num;
      shift(@line_nums) if @line_nums && $line_nums[0] == $line_num;
      next;
   }

   last unless @line_nums;
   $line_num = shift(@line_nums);
   $more = 2;
}
[download]

Tested:

• Handles overlap. For example, asking for lines 1, 2 & 4 prints lines 1, 2, 3, 4, 5 & 6.
• Handles end of file. For example, asking for line 15 of a file with 16 lines prints lines 15 and 16 (and doesn't give an error for the missing line 17).

Features:

• Efficient. Only looks at one element of @line_nums per line of the input file.
• Efficient. Stops reading the input file if there are no more lines to print.

Limitations:

• Assumes @line_nums is sorted. This assumption is easy to remove.

To do:

• Read the line numbers one at a time, instead of having them all in memory.