uptoqdigits(n) = {
	qchecks = 0; 
	maxqd = n; 
	pd = vector(n+1, i, possibledigits(i));
	pow10s = vector(n, i, 10^(i));
	my(i);
	res = List(); 
	for(i = 1, 9, 
		process(i, 1);
		print(qchecks);
	);
	Set(res);	
}

process(n, qd) = {
	qchecks++;
	if(issquare(n),
		listput(res, n); 
	);
	if(!issquare(Mod(n, 10^(qd))),
		return
	);
	my(cn, cqd = qd + 1, i);
	if(qd >= maxqd,
		return
	);
	for(i = 1, #pd[qd+1],	
		cn = pow10s[qd] * pd[qd+1][i] + n;
		process(cn, cqd)
	);
}


possibledigits(n) = {
	if(n == 1, return([1..9]));
	my(d = divisors(n), res = List());
	if(d[2] > 9,
		return(List([1]));
	);
	for(i = 2, #d, 
		if(d[i] < 10,
			listput(res, d[i])
		,
			break
		)
	);
	for(i = 2, 9\n,
		listput(res, n*i); 
	);
	res
}