big = 1 000 000
s = 0
S = Set([])
unseen = 1
seen(v) = if (v < big, bit test(s, v), set search(S, v))
see(v) = if (v < big, s = bit or(s, 2^v), S = set union(S, Set([v]))); while (seen(unseen), unseen++)

ok(x,y) = my (f=factor(x*y)); sum(i=1, #f~, hammingweight(bitxor(valuation(x,f[i,1]), valuation(y,f[i,1]))))==1

other(p) = {
	see(p);
	fordiv (p, d,
		if (!seen(d) && ok(p,d),
			return (d);
		);
	);
	forstep (m=2*p, oo, p,
		if (!seen(m) && ok(p,m),
			return (m);
		);
	);
}

v=1; for (n=1, 10 000, print (n " " v); v=other(v))

quit