big = 1 000 000
s = 0
S = []
unseen = 1
seen(v) = if (v < big, bittest(s, v), setsearch(S, v))
see(v) = if (v < big, s = bitor(s, 2^v), S = setunion(S, [v])); while (seen(unseen), unseen++)

\\ least k unseen / gcd(p, k) != 1
look(p) = {
	for (v = unseen, oo,
		if (!seen(v) && gcd(p, v)!=1,
			return (v);
		);
	);
}

b = vector(10 000)
u = 1

n = 0
a = [0]
emit(v) = {
	n++;

	if (v <= #b,
		b[v] = n;
		while (b[u],
			print (u " " b[u]);
			if (u++ > #b,
				quit;
			);
		);
	);

	see(v);
	if (#a < n,
		a = concat(a, vector(#a));
	);
	a[n] = v;
}

{
	emit(1);
	emit(2);
	for (n = 2, oo,
		emit(v = look(a[n]));
		emit(look(gcd(v, a[n])));
	);
}

quit