my %present = ();		# numbers already present
my $binary_repr = "";	# binary representation so far
my $zeroone_repr = "";	# 0 and 1 from decimal representation so far

sub compute_next_term {
	my $try = 1;
	while (1) {
		if (exists $present{$try}) {
			# already seen
		} else {
			my $binary = sprintf("%b", $try);
			my $zeroone = "$try";
			$zeroone =~ s,[^01]+,,g;

			if (substr($binary_repr . $binary,
			           0, length($zeroone_repr) + length($zeroone))
							 ne ($zeroone_repr . $zeroone)) {
				# contradiction
			} else {
				$present{$try} = 1;
				$binary_repr .= $binary;
				$zeroone_repr .= $zeroone;
				return $try;
			}
		}

		$try++;
	}
}

foreach my $n (1..10_000) {
	print $n, " ", compute_next_term(), "\n";
}