What have you tried thus far? You just need to use regex's to compare mate:

use strict;

my @last;
my $lastKey;
while (<DATA>) {
    my @rec = /(\S+)/;
    my ($key) = $rec[0] =~ m/([^#]+)/;

    if ($key eq $lastKey) {
        print "matching $key\n";
    }

    @last = @rec;
    $lastKey = $key;
}

__DATA__
HWUSI-EAS95L_0025_FC:3:1:5232:1082#0/1 - 1449586 1449619
HWUSI-EAS95L_0025_FC:3:1:5232:1082#0/2 - 1449544 1449577
HWUSI-EAS95L_0025_FC:3:1:6417:1078#0/1 - 4744083 4744113
HWUSI-EAS95L_0025_FC:3:1:6539:1083#0/1 - 4867122 4867157
HWUSI-EAS95L_0025_FC:3:1:6539:1083#0/2 - 4866942 4866977
HWUSI-EAS95L_0025_FC:3:1:10260:1083#0/1 + 1930232 1930266
HWUSI-EAS95L_0025_FC:3:1:10260:1083#0/2 + 1930354 1930389
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