A031349 3-multiplicative persistence: number of iterations of "multiply 3rd powers of digits" needed to reach 0 or 1.

0, 4, 5, 4, 3, 4, 4, 3, 3, 1, 1, 4, 5, 4, 3, 4, 4, 3, 3, 1, 4, 4, 4, 3, 2, 3, 4, 2, 3, 1, 5, 4, 3, 3, 4, 3, 4, 3, 4, 1, 4, 3, 3, 2, 2, 3, 3, 3, 3, 1, 3, 2, 4, 2, 3, 2, 3, 2, 3, 1, 4, 3, 3, 3, 2, 3, 2, 2, 3, 1, 4, 4, 4, 3, 3, 2, 4, 3, 2, 1, 3, 2, 3, 3, 2, 2, 3, 3, 3, 1, 3, 3, 4, 3, 3, 3, 2, 3, 3