Reverse factorial at Lua...

defac.lua

-- defac as multi-dispatch pseudo-code
--
-- defac(x):    defac(x / 1, 1)     [ where x is Integer ]
-- defac(x, d): d - x               [ where x = 1 ]
-- defac(x, d): error()             [ where x < 1 ]
-- defac(x, d): defac(x / d, d + 1) [ where x > 1 ]

function defac (x, d)
  d = d or 1
  if x == 1 then
    return d - 1
  elseif x < 1 then
    error ("Sorry, X isn't a factorial number.")
    return
  else
    local r = defac (x / d, d + 1)
    return r
  end
end

-- test
print (defac (24)) --> 4
print (defac (720)) --> 6
print (defac (120)) --> 5
print (defac (121)) --> error!

-- end of script