Given a number, find notation bases for which number is palindrome

bday-palindrome

-- e.g. Find bases for which bday is palindre: findPal YYYYMMDD [2..1000]
-- or compile and run: echo YYYYMMDD | bdaypalbase

findPal bases n =
  filter (Nothing /=) [isPal n b | b <- bases]

isPal n b =
  if pal then Just (n, b, digits) else Nothing
  where
    digits = toDigits n b
    (h1, h2) = toHalves digits
    pal = h1 == (reverse h2)

toDigits n base =
  let toBase_ n b l | n < b = n:l
      toBase_ n b l         = let (q,r) = n `quotRem` b
                              in toBase_ q b (r:l)
  in toBase_ n base []

toHalves l@(_:_:cs) =
  (h1, stripcenter h2)
  where
    (mid, odd) = (length l) `quotRem` 2
    stripcenter = if odd == 1 then tail else id
    (h1, h2) = splitAt mid l

main =
  interact (show . map ((\i -> findPal [2..i] i) . read) . lines)