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););););); }

todualzeck0(n) = { my (s=0, v=0); for (i=0, oo, if (s>=n, forstep (j=i-1, 0, -1, if (s-fibonacci(2+j)>=n, s-=fibonacci(2+j); v-=2^j;);); return (v);); s+=fibonacci(2+i); v+=2^i;); }

cache = [todualzeck0(1)]

todualzeck(n) = {
	while (#cache < n,
		cache = concat(cache, apply (todualzeck0, [#cache+1, 2*#cache]));
	);
	if (n, cache[n], 0);
}

s = 0
unseen = 1
seen(v) = bittest(s, v)
see(v) = s = bitor(s, 2^v); while (seen(unseen), unseen++)

other(n) = {
	my (zn = tozeck(n));
	for (v = unseen, oo,
		if (!seen(v) && bitand(todualzeck(v), zn)==0,
			see(v);
			return (v);
		);
	);
}

{
	a = vector(10 000);
	u = 1;

	print ("0 0");
	for (n = 1, oo,
		v = other(n);
		if (v <= #a,
			a[v] = n;
			while (a[u],
				print (u " " a[u]);
				if (u++ > #a,
					break (2);
				);
			);
		);
	);
}

quit