Sorry, I got a bit tied up with something! Try something like this - your data is in an array but otherwise....

use strict;
use warnings;

my ($i, @array, $bin, $line);

my @input = (
"5893    5985    + LOC645399 645399",
"7223    7231    - LOC100131533  100131533",
"7630    9882    - LOC100131533  100131533",
"10142    11428    + LOC100132836  100132836",
"12197    13705    - LOC100132070  100132070",
"14248    15806    - LOC100132865  100132865",
"16830    17405    - LOC100132865  100132865",
"18735    19817    + LOC645399  645399",
"20802    23113    - LOC100132865  100132865"
);

for ($i = 5893; $i <=23113; $i++) { 
    $bin = $i += 7704; 
    push @array, $bin ; 
} 

foreach $line (@input) { 
    $line =~ m/\s*(\d+)\s*(\d+)/;
    foreach my $bin (@array) {
        if (($bin >= $1) && ($bin <= $2)) {
            print "$1 $2\n";
            last;
        } 
    }
}
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