my @nums=qw(16 107 108 110 112 114 115 117 118 119 120 121 122 123 124
+ 125 127 128 130 132 133 135 136 138 142 146 149 150 154 156 157 158 
+159 161 162);

my $limit=4;

my $direction=1;

my @cont=get_cont($limit,$direction,@nums);

if(@cont>0)
    {
    print "First continuous block of $limit numbers in ",$direction>0?
+"ascending":"descending"," direction is: ",join(',',@cont);
    }
else
    {
    print "No block was found.\n";
    }

sub get_cont
{

my $limit=shift;

my $dir=shift;

my @nums=@_;

my $prev;
my @cont;

for $num (@nums)
    {
    
    if(($num-$prev)==$dir)
        {
        push(@cont,$num);
        
        if(@cont>=$limit)
            {
            return @cont;
            }
        }
    else
        {
        @cont=();
        }
        
    $prev=$num;
    
    }
    
return ();
}
[download]

Change $limit to 2500 for your real data (and direction to -1 if you want continuous blocks of descending numbers).