allocate mem(2^30)

bits(n) = {
	my (b=vector(hammingweight(n)));
	for (k=1, #b,
		n -= 2^(b[k] = valuation(n, 2));
	);
	b
}

o = select(v -> hammingweight(v)%2, [0..M=2^16])
cache = apply(bits, [0..M])
bits(n) = cache[1+n]

T(n,k) = {
	my (nn=bits(o[n]), kk=bits(o[k]), v=0);
	for (i=1, #nn,
		for (j=1, #kk,
			v=bitxor(v, 2^bitxor(nn[i], kk[j]));
		);
	);
	my (w=setsearch(o, v));
	if (w, return (w), quit);
}

print (0 " " f=1)
for (n=1, #o, print (n " " f=T(f, n)))

quit