If a language is either finite or in infinite Arithmetic Progression then it is Regular.
Why finite? Because Finite Automata has finite memory.
Why infinite AP? Because then there is a pattern that can be implemented in a finite number of states without the help of a stack. Other kind of infinite patterns like Prime Numbers, Geometric Progression, Harmonic Progression, etc. can't be implemented in finite number of states without using stack. So basically, this AP point is also concluded from the fact of finite memory is associated but stack is not associated with Finite Automata to realise a regular language.
Other kind of rare examples include languages like:
L={ wxw | w,x € (0,1)* }
