s = 0
unseen = 0
seen(v) = bit test(s, v)
see(v) = s = bit or(s, 2^v); while (seen(unseen), unseen++)

tozeck(n) = {
	for (i=0, oo,
		if (n<=fibonacci(2+i),
			my (v=0, f);
			forstep (j=i, 0, -1,
				if (n>=f=fibonacci(2+j),
					n-=f;
					v+=2^j;
				);
				if (n==0,
					return (v);
				);
			);
		);
	);
}

cache = apply(tozeck, [0..12 000])

other(p) = {
	see(p);
	my (pp=cache[1+p]);
	for (v=unseen, oo,
		if (!seen(v) && bitand(pp, cache[1+v])==0,
			return (v);
		);
	);
}

for (n=0, 10 000, print (n " " v=if (n==0, 0, other(v))))

quit