SimpleStack on TIO, 6 bytes

(.%@9)

This requires that the input box on TIO is empty.

(.%@9)
(....)  loop while top of stack truthy
 .       increment top of stack (read input if stack empty)
  %      print
    @9    output HTAB (decimal 9)

SimpleStack, 8 7 bytes

1(%@9.)
1        push 1 (only works at start of program)
 (....)  infinite loop
  %       print top of stack
   @9     print tab
     .    increment

Implicit on TIO, 6 4 bytes

(.%ß

This requires that the input box on TIO is empty.

(.%ß
(...   « loop while top of stack truthy                       »;
 .     «  increment top of stack (read input if stack empty)  »;
  %    «  print integer                                       »;
   ß   «  print space                                         »;
       « just kidding, loop forever                           »;

Try it online!

SimpleStack on TIO, 6 bytes

(.%@9)

This requires that the input box on TIO is empty.

(.%@9)
(....)  loop while top of stack truthy
 .       increment top of stack (read input if stack empty)
  %      print
   @9    output HTAB (decimal 9)

SimpleStack, 8 bytes

:1(%@9.)

I really need a better way to push ints...

:1        push 1
   (....)  infinite loop
   %       print top of stack
    @9     print tab
      .    increment

SimpleStack on TIO, 6 bytes

(.%@9)

This requires that the input box on TIO is empty.

(.%@9)
(....)  loop while top of stack truthy
 .       increment top of stack (read input if stack empty)
  %      print
   @9    output HTAB (decimal 9)

SimpleStack, 8 7 bytes

1(%@9.)
1        push 1 (only works at start of program)
 (....)  infinite loop
  %       print top of stack
   @9     print tab
     .    increment