a = vector(1000, n, oo)

maxk = 13

explore(v, k) = {
	if (v<=#a,
		a[v] = min(a[v], k);
	);

	if (k++<=maxk,
		my (d=digits(v));
		for (i=1, #d,
			if (d[i],
				for (j=i, #d,
					my (s=fromdigits(d[i..j]));

					explore(fromdigits(concat([d[1..i-1], digits(2*s), d[j+1..#d]])), k);

					if (s%3==1,
						my (z=(s-1)/3);
						if (z%2,
							explore(fromdigits(concat([d[1..i-1], digits(z), d[j+1..#d]])), k);
						);
					);
				);
			);
		);
	);
}

{
	explore(1, 0);

	for (n=1, #a,
		if (a[n]==oo,
				break,
				print (n " " a[n]);
		);
	);
}

quit