Shift register with initial value 1
Some shift registers allow a parallel load. If so, you can just wire up your default case and at power-on reset cause a load to take place. Or you can use the set input of the first FF, I suppose.

But a Johnson counter with decoding is what's often done. You can look at the  CD4022B, for an example. The schematic also includes a so-called "disallowed state detector" made out of an AND and NOR gate, as well.