I liked this little puzzle so much I thought I'd chuck it out to my local radio club and see what kind of answers I would get.
I didn't specify any limitations at first so that the foundation licence guys could have a go at it.
First suggestion was of course to use a PIC, which I removed the MCU possibility.
Then a ROM. Which is what most of the members said they would do since they don't program MCU's.
Then it was down to a simple counter like a 4017 with a diode array.
Then a binary (mod8) counter with logic gates.
Finally I suggested that they could only do it with flip flops. (not logic gates allowed)
It stumped most people because they couldn't work around the exclusion of any logic gates at all.
Nobody made the jump to twisted ring or scrambled bit counters. I did, see the previous post (#9).
I have also considered a Pseudo Noise shift register, but I'm not able to find a 4 bit winning combination to generate this sequence.
One comes close with a nand function to correct the "9" digit.