(*
  AUTHOR: Eugene Wallingford
  DATE  : 2019/09/10

  This program determines if its argument, a number n, is "special"
  as defined by James Tanton:

  https://twitter.com/jamestanton/status/1042393711014031360

  |  N is "special" if, in binary, N has a 1s and b 0s and a & b are
  |  each factors of N (so non-zero).  The first few special numbers
  |  are: 2, 4, 6, 8, 10, 12, 16, 18.

  I don't think 8 is special, though it's my favorite number.
*)

(*--------------------------------------------------------------------*)

function MOD( m : integer, n : integer ) : integer
  (* standard library function *)
  m - m/n * n

(*--------------------------------------------------------------------*)

function divides(x : integer, n : integer) : boolean
  (* returns true if x is a factor of n, for 0 < x <= n *)
  MOD(n, x) = 0

function count(bit : integer, n : integer) : integer
  (* returns the number of time bit occurs as a digit in n. *)
  (* intended use is for bit in (0,1) and a binary n        *)
  if n < 10 then
     if bit = n then 1 else 0
  else
      if bit = MOD(n, 10)
         then 1 + count(bit, n/10)
         else count(bit, n/10)

function to_binary(n : integer) : integer
  (* converts a decimal number n to its binary equivalent *)
  if n = 0
     then 0
     else 10 * to_binary(n/2) + MOD(n,2)

(*--------------------------------------------------------------------*)

function apply_definition(binary_n : integer, n : integer) : boolean
  (* computes the definition of is_special?, for binary number bin_n *)
  divides(count(1, binary_n), n) and
  divides(count(0, binary_n), n)

function main( n : integer ) : boolean
  apply_definition(to_binary(n), n)