Can a PROM and Shift Register Recognize Specific Number Sequences?

[some_one]

i need to implement a sequential circuit that has two outputs
the first recognizes 1,4,5,9
the second one recognizes 12,13,14,15
i need build this one using a PROM and a shift register

 

[some_one]

what should i do...

i think that a shift register is just a slow input line
it proceeds in each Clock pulse were in normal line they data comes straight away.i was required to use it in the question

i don't have any idea of how to build this thing

when i tried to build the situation table
i came to the conclusion that building it in the normal way with flip flops
its impossible.its a 4 bit number
there are lots of possibilities
it would take me hours to write each one

i think they intended for some other solution

what should i do??