m/\A
  (?:
     [1]\d+  # if it starts with a 1,
             # it has to be followed by other digits
     |
     [023456789]\d* # otherwise one digit can be fine
  )
  \z
/x
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Note that this matches only non-negative integers, and 01 is matched as well (no idea if that's OK or not, spec is unclear).

Note that you need some kind of anchoring (perhaps to a word boundary), but you don't necessarily need to anchor it to start and beginning of the string.