These files contain minimal finite automata that compute the nth Motzkin number modulo various prime powers. In particular, they show that no Motzkin number is divisible by 2³, 5², 13², 31², or 37². They were computed with my package IntegerSequences. See my paper with Reem Yassawi for more details.

• modulo 2³ (24 states) and modulo 2⁶ (701 states)
• modulo 3⁵ (3866 states)
• modulo 5² (136 states) and modulo 5³ (2797 states)
• modulo 7² (317 states) and modulo 7³ (12300 states)
• modulo 13² (2097 states)
• modulo 31² (28081 states)
• modulo 37² (44173 states)

These automata can be also computed by another method, described in my paper with Doron Zeilberger and implemented in his package AutoSquared.