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UberGenes, 66 bytes

=ii+a1=l0-l2=pa=z8*z6=t5*t2=bi=qp%qt+qz=Lq-l1/pt:bp=bi=oL+l1:bL=i0

Prints the numbers separated by NULLs. Integers and memory in UberGenes are bounded only by computer memory, so it meets the "forever" requirement.

How it works (indents indicate a loop start):

=ii                                  NOP
   +a1                               INC a (initially 0)
   =l0-l2                            SET l=-2
   =pa                               COPY a INTO p
   =z8*z6                            SET z=48 ('0')
   =t5*t2                            SET t=10
   =bi                               SET b to this location (27)
      =qp                            COPY p INTO q
      %qt                            MOD q BY 10
      +qz                            ADD 48 to q (turn it into character)
      =Lq                            PUT q AT MEM[l]
      -l1                            DEC l
      /pt                            DIVIDE p by 10
      :bp                            JUMP back to b's location if p>0
   =bi                               SET b to this location (51)
      =oL                            OUTPUT the character in MEM[l]
      +l1                            INC l
      :bL                            JUMP back to b's location if MEM[l]>0
   =i0                               JUMP back to beginning of main loop