To avoid reading the whole table into a hash, consider using substrings within the SQL to match the sequences. For example

#!/usr/bin/perl
use strict;
use DBI;
use Data::Dumper;
my $n = 6;

unlink 'mytestdb.sqlite' if -e 'mytestdb.sqlite';
my $dbh = DBI->connect("dbi:SQLite:dbname=mytestdb.sqlite","","");

test_setup();

my $sql2 = "
  SELECT id,seq,substr(seq,1,$n),substr(seq,-$n)   
  FROM testtable 
  WHERE id IN ('55436','56875','56789')";
  
my $ar = $dbh->selectall_arrayref($sql2);  
  
my $sql3 = "
  SELECT id
  FROM testtable
  WHERE substr(seq,1,$n) = ? 
    AND substr(seq,-$n) = ?
    AND id != ?";
  
my $sth3 = $dbh->prepare($sql3);

my @output = ();
my $i=0;
for my $rec (@$ar){ 
  $sth3->execute($rec->[2],$rec->[3],$rec->[0]);
  my $others = join ',',
               map { $_->[0] } 
               @{ $sth3->fetchall_arrayref() };
  push @output,[++$i,$rec->[0],$others];
}
print Dumper \@output;

sub test_setup {
  $dbh->do('CREATE TABLE testtable (id,seq)');

  my $sth = $dbh->prepare('INSERT INTO testtable VALUES (?,?)');
  while (<DATA>){
    chomp;
    my @f = split ", ",$_;
    $sth->execute(@f);
  }
}          

__DATA__
55436, atcgtggtcgtgt
56875, agtcgtagtctaa
56789, tgatgcgtctatc
23698, atcgtgctcgtgt
75699, tgatgcttctatc
87226, atcgtgatcgtgt
12214, agtcgttgtctaa
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