unseen = 0
tr(v)=if (v>=0, 1+2*v, -2*v)
s = 0
seen(v) = my (w=tr(v)); bittest(s,w)
see(v) = my (w=tr(v)); s=bitor(s,2^w); while (seen(unseen) && seen(-unseen), unseen++)

n = -1
emit(v) = {
	see(v);
	print (n++ " " v);
	last v = v;
}

{
	emit(0);

	for (n = 1, 5 000,
		\\ up
		for (x = 1, oo,
			w = last v + x^2;
			if (w > 0 && !seen(w),
				emit(w);
				break;
			);
		);
		\\ down
		for (x = 1, oo,
			w = last v - x^2;
			if (w < 0 && !seen(w),
				emit(w);
				break;
			);
		);
	);
}

quit