\\ zeckendorf representation
tozeck(n, base=10) = {
	for (k=2, oo,
		if (fibonacci(k)>=n,
			my (v=0);
			while (n,
				if (n>=fibonacci(k),
					v+=base^(k-2);
					n-=fibonacci(k);
					k--;
				);
				k--;
			);
			return (v);
		);
	);
}

prof(n) = my (z=tozeck(n, 2)); #binary(z) + hammingweight(z)*I

mx = fibonacci(21)-1

pp = Set(apply(prof, [0..mx]))
vv = vector(#pp, n, [])
nb = vector(#pp)

for (n=0, mx, i=setsearch(pp, prof(n)); vv[i]=concat(vv[i], n); nb[i]++)

for (n=0, mx, i=setsearch(pp, prof(n)); print (n " " v=vv[i][nb[i]]); nb[i]--)

quit