a = vector(2^13)

match(k, b) = {
	for (i=2, #b,
		if (k%2 != b[i],
			return (0);
		);
		if (a[k]==0,
			my (bk=binary(k));
			my (r=#b-i);
			for (j=1, r,
				if (b[i+j]!=bk[1+j],
					return (0);
				);
			);
			return (1);
		);
		k = a[k];
	);
	return (1);
}

search(n) = {
	my (b=binary(n));

	for (k=1, oo,
		a[n] = k;
		if (match(k, b),
			return;
		);
	);
}

for (n=1, #a, search(n); print (n " " a[n]))

quit