Hello,

If it were 2 or 3 steps (or a multiple), the periodicity of a state will be the gcd of 2 and 3. This is merely the definition of a period But here, you can have 5 steps : 0 - 1 - 2 - 1 - 2 - 0. So actually, the period will be 1.

Transience and periodicity have no relationship, there is no period associated to a transient state.