Repunits whose digits in base $b$ are all $b-1$

Question

Positive integers whose base-$b$ representation contains only the digit $1$ are called repunits in that base. But what about positive integers whose base-$b$ representation contains only the digit $b-1$?

For instance, how would one call the base-$20$ number whose representation in that base is $$19\cdot19\cdot19\cdot19\cdot19_{20}?$$

Is there a special name for this kind of number? I know repunits are useful in many number-theoretical contexts, but what about such numbers?

Answer 1

While there is no name, to my knowledge, for the general case, they are referred to as Mersenne numbers for base 2.