can add(x,y) = {
	for (r=2, oo,
		if (x==0 || y==0,
				return (1),
			floor(x)+floor(y)>=r-1,
				return (0),
				x=frac(x)*r;
				y=frac(y)*r;
		);
	);
}

{
	print (k++ " " 1);
	tot = 0;

	while (1,
		rem = 1-tot;
		for (n=max(2, floor(1/rem)), oo,
			if (can add(tot, 1/n),
				tot+=1/n;
				print (k++ " " n);
				break;
			)
		)
	)
}

quit