/* 

  Euler #46 in Picat.

  """  
  It was proposed by Christian Goldbach that every odd composite number can be 
  written as the sum of a prime and twice a square.

  9 = 7 + 2×1^2
  15 = 7 + 2×2^2
  21 = 3 + 2×3^2
  25 = 7 + 2×3^2
  27 = 19 + 2×2^2
  33 = 31 + 2×1^2

  It turns out that the conjecture was false.

  What is the smallest odd composite that cannot be written as the 
  sum of a prime and twice a square?
  """


  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

main => go.

go => time(euler46).

euler46 =>
  Res = 0,
  GotIt = 0,
  foreach(I in 3..2..10000, not prime(I), GotIt == 0)
    S = round(sqrt(I/2)),
    Found = 0,
    foreach(J in 1..S, Found == 0)
      Ts = J*J*2,
      if prime(abs(I-Ts)) then
        Found := 1
      end
    end,
    if Found == 0 then
      Res := I,
      GotIt := 1
    end
  end,

  println(res=Res).