3n+1 Ep69: What's the fate of 7 under the 5n+1 rule?

It's a longstanding conjecture than 7 never reaches 1 under the 5n+1 rule. 007 seems to be on a bumpy road to infinity, but who knows? Here's a 16-state program that stops iff 7 reaches 1, which would refute the conjecture. If the program runs for BB(16) steps, it will never stop, which would confirm the conjecture. What's the smallest program that achieves the same goal? #collatz initial A, accept Z, A _ L 1 r, B _ B _ r, B 1 C 1 r, C _ Z _ l, C 1 D 1 r, D _ F 1 l, D 1 E 1 r, E _ K _ l, E 1 D 1 r, F 1 G _ l, F _ F _ l, G 1 H _ l, H _ J _ r, H 1 I 1 r, I _ I _ r, I 1 D 1 l, J _ J _ r, J 1 B 1 l, K _ L _ r, K 1 L _ r, L _ M _ r, L 1 L 1 r, M _ N 1 l, M 1 N 1 r, N _ M 1 r, N 1 O 1 l, O _ P 1 l, O 1 O 1 l, P _ B 1 l, P 1 L _ r This program can be tested at alistat dot eu slash online slash turingmachinesimulator. Reference on Erdos conjecture: "On the hardness of knowing busy beaver values BB(15) and BB(5,4)" (Tristan Stérin, Damien Woods), 2021.