toprim(n) = my (d=[]); forprime (p=2, oo, if (n==0, return (d), d=concat(n%p,d); n\=p))

classify(n) = if (n==0, 0, vecsum(toprim(n)))

{

	for (w=0, 6,
		mi = if (w==0, 0, prod(k=1,w-1,prime(k)));		\\ smaller number with w digits
		mx = prod(k=1,w,prime(k))-1;					\\ greatest number with w digits

		if (#toprim(mi)!=w || #toprim(mx)!=w,
			print ("#oops");
			print (mi " " toprim(mi));
			print (mx " " toprim(mx));
			quit
		);

		vv = [mi..mx];				\\ numbers with w digits
		cl = apply(classify, vv);	\\ corresponding classes
		cc = Set(cl);				\\ all classes
		mm = vector(#cc, c, []);	\\ members by class

		for (k=1, #vv,
			c = setsearch(cc, cl[k]);
			mm[c] = concat(mm[c], vv[k]);
		);

		nb = vector(#cc);			\\ # of members seen so far by class

		for (k=1, #vv,
			c = setsearch(cc, cl[k]);
			print (vv[k] " " mm[c][#mm[c]-nb[c]]);
			nb[c]++;
		);
	);
}

quit