Veit Elser: "Have you considered generalizing to sentences where each letter appears exactly twice? It should still be a challenge, but will improve the likelihood of being able to form a coherent statement." For a year I've been playing with this concept applied to factorization "sentences" in base ten. The letters are of course the ten digits. A sentence is an integer equated to its normally expressed factorization (greater-than-one powers of strictly increasing primes). No leading zeros. When each digit appears exactly k times, the sentences may be said to be "k-balanced". https://oeis.org/A273260 There are 4 solutions for k = 1 and 13022 solutions for k = 2. I recently showed that 4546782683595318279169 (= 7^10 * 2003^4) is the largest integer leading to a k = 3 solution (785984586660 is the smallest) and 19260075803546226131439208984375 (= 5^18 * 7 * 947^6) is the largest integer leading to a k = 4 solution (we'll likely never know the smallest). I have a solution for k = 13. Can you find a larger one?