my %delta = ();	# already occured in first difference ?
my %seen  = ();	# already occured in sequence ?

sub other {
	my $prev = shift;
	$seen{$prev} = 1;

	my $d = -int(sqrt($prev));
	while (1) {
		if (not exists $delta{$d**2}) {
			my $i = $prev + $d * abs($d);
			if ($i>0 && not exists $seen{$i}) {
				$delta{$d**2}++;
				return $i;
			}
		}

		$d++;
	}
}

my $a = 1;
foreach my $n (1..100_000) {
	print "$n $a\n";
	$a = other($a);
}