Binary Counter not synchronous
Any 4-bit binary counter will do the job, but you need to alter the output.

Complex, but "normal" way - a nice logic circuit involving lots of gates to convolve the 4 bits of synchronous counting into the sequence you want.  Tricky, but possible with some nice Karnaugh mapping to get you through.

Simple, but "alternative" way - Counter + small (E)EPROM.  Counter drives the address lines of the (E)EPROM.  Data lines of the (E)EPROM contain the modified count values.  The beauty of this way is that a) it's low on component count, and b) a new number sequence can be programmed without needing to change the circuitry in any way.