use strict;
use warnings;


sub find_seq {
    my ($num,$array)=@_;

    # assert that @$array is sorted numerically increasing

    return unless $num<=@$array; # illegal

    $num--;  # num is one based, we need a 0 based value
    my $min_pos=$num;
    my $min=$array->[$min_pos] - $array->[0];

    for my $i ($num..$#$array) {
        if ($array->[$i] - $array->[$i-$num] == $num) {
            return ($i-$num,$i);
        } elsif ($min > $array->[$i]-$array->[$i-$num]) {
            $min=$array->[$i] - $array->[$i-$num];
            $min_pos=$i;
        }
    }
    return ($min_pos-$num,$min_pos);
}

my @array=sort { $a <=>$b } qw( 1 3 4 5 6 8 15 31  
                                61 62 63 64 65 66 67 
                                70 71 72 73 );

for my $num (2..@array-5) {
    if (my ($s,$f)=find_seq($num,\@array)) {
        print "seq($num) == \@array[$s..$f]=(",
              join(",",@array[$s..$f]),")\n";
    } else {
        print "No sequence for $num\n";
    }
}
__END__
seq(2) == @array[1..2]=(3,4)
seq(3) == @array[1..3]=(3,4,5)
seq(4) == @array[1..4]=(3,4,5,6)
seq(5) == @array[8..12]=(61,62,63,64,65)
seq(6) == @array[8..13]=(61,62,63,64,65,66)
seq(7) == @array[8..14]=(61,62,63,64,65,66,67)
seq(8) == @array[8..15]=(61,62,63,64,65,66,67,70)
seq(9) == @array[8..16]=(61,62,63,64,65,66,67,70,71)
seq(10) == @array[8..17]=(61,62,63,64,65,66,67,70,71,72)
seq(11) == @array[8..18]=(61,62,63,64,65,66,67,70,71,72,73)
seq(12) == @array[7..18]=(31,61,62,63,64,65,66,67,70,71,72,73)
seq(13) == @array[6..18]=(15,31,61,62,63,64,65,66,67,70,71,72,73)
seq(14) == @array[1..14]=(3,4,5,6,8,15,31,61,62,63,64,65,66,67)

##</code><code>##

sub find_seq {
    my ($num,$array)=@_;

    # assert that @$array is sorted numerically increasing

    return if $num > @$array; # ensure array is big enough
           

    $num--;  # num is one based, we need a 0 based value
    
    # the default return will be the first N values,
    # if we find better then we will overwrite these
    my $min_start = 0;
    my $min_end = $num;
    my $min = $array->[$num] - $array->[0];

    # start at num as below that nothing can match
    for my $end ( $num .. $#$array) {
        my $start = $end - $num;
        my $diff = $array->[$end] - $array->[$start];
        if ( $min > $diff ) {
            # we have found a better sequence, 
            # so remember where it is
            $min = $diff;
            $min_end = $end;
            $min_start = $start;
        }
        # if the sequence is contiguous we can finish
        last if $diff == $num; 
    }
    return ( $min_start, $min_end );
}