contains(x,y) = {
	my (m=10^#digits(y));
	while (x>=y,
		if (x%m==y,
			return (1),
			x\=10;
		);
	);
	return (0);
}

odd part(n) = n/2^valuation(n,2)

slot = [1]	\\ next value by odd part
unseen = 1	\\ unseen value

seen(v) = {
	my (o=odd part(v));
	while (#slot < o,
		slot = concat(slot, vector(#slot, k, k+#slot));
	);
	slot[o] > v;
}

other chain() = {
	my (c=unseen);
	for (x=1, oo,
		if (contains(c*=2, unseen),
			my (chain = unseen * powers(2, x));

			slot[odd part(unseen)] *= 2^(x+1);
			while (seen(unseen),
				unseen++;
			);

			return (chain);
		);
	);
}

for (c=1, 10 000, print (c " " #other chain()))

quit