/*
  Goldbach's other conjecture
  Problem 46
  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 + 2×12
        15 = 7 + 2×22
        21 = 3 + 2×32
        25 = 7 + 2×32
        27 = 19 + 2×22
        33 = 31 + 2×12

  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?
*/

const fp = require('lodash/fp');
const object = require('lodash/fp/object');
const extend = require('lodash/fp/extend');

const isPrime = require('is-prime-number');

function isTwiceSquare(n) {
  let squareTest = Math.sqrt(n/2);
  return squareTest === Math.round(squareTest);
}

let primes = fp.filter(isPrime)(fp.range(1,10000));

// c-p = 2*x**2
function compute(){
  let c = 1;
  let notFound = true;

  while(notFound){
    c += 2;

    let j = 0;
    notFound = false;
    while (c >= primes[j]) {
      if(isTwiceSquare(c-primes[j])){
        notFound = true;
        break;
      }
      j++;
    }
  }
  return c; //5777
}