各桁の和が3の倍数な整数は3の倍数 in Egison

multiOf3-N.egi

;; > egison -N
;; > loadFile("multiOf3-N.egi")


def sumMulti?(x, n2, y) =
  match (sum(map(($i -> x_i), 1..n2)) + y) as mod(3)
    | 0 -> #t
    | _ -> #f

def afterCheck?(ans) =
  all(($k -> k % 3 == 0), map(foldl(2#(%2 + 10 * %1), 0, $), ans))

def calcMultiOf3'(n) =
  matchAll cons(1..9, take((n-1), repeat1(0..9))) as list(multiset(integer))
    | _ <++>
      loop($i, (1, [n-1], _), <cons ($x_i <:> _) ...>,
                              <cons ((?sumMulti?(x, (n-1), $) and $y) <:> _) <nil>>) ->
        [@map(($i -> x_i), 1..(n-1)), y]
def calcMultiOf3(n) =
  let ans = calcMultiOf3'(n)
  in (ans, afterCheck?(ans))

def resultMultiOf3(n) = snd(calcMultiOf3(n))