gremlin_2

gremlin_2.js

function FIB(n) {
	phi = (1 + Math.sqrt(5))/2
	eta = (1-phi)
	return (Math.pow(phi,n) - Math.pow(eta,n)) / Math.sqrt(5)
}

var j = 0

for (var i = 5;i < 500;i++) {
	var num = FIB(i)
	if (num >= 227000 && isPrime(Math.round(num))) {
		j = Math.round(num);
		break;
	}
}

function isPrime(n) {
 if (isNaN(n) || !isFinite(n) || n%1 || n<2) return false; 
 if (n==leastFactor(n)) return true;
 return false;
}

x = primeFactorList(j+1).reduce(function(a,b) {
	return a+b
},0);

console.log(x);

// leastFactor(n)
// returns the smallest prime that divides n
//     NaN if n is NaN or Infinity
//      0  if n=0
//      1  if n=1, n=-1, or n is not an integer
function leastFactor(n){
 if (isNaN(n) || !isFinite(n)) return NaN;  
 if (n==0) return 0;  
 if (n%1 || n*n<2) return 1;
 if (n%2==0) return 2;  
 if (n%3==0) return 3;  
 if (n%5==0) return 5;  
 var m = Math.sqrt(n);
 for (var i=7;i<=m;i+=30) {
  if (n%i==0)      return i;
  if (n%(i+4)==0)  return i+4;
  if (n%(i+6)==0)  return i+6;
  if (n%(i+10)==0) return i+10;
  if (n%(i+12)==0) return i+12;
  if (n%(i+16)==0) return i+16;
  if (n%(i+22)==0) return i+22;
  if (n%(i+24)==0) return i+24;
 }
 return n;
}

function primeFactorList(n) {
	if (n < 1)
		throw "Argument error";
	
	var result = [];
	while (n != 1) {
		var factor = leastFactor(n);
		result.push(factor);
		n /= factor;
	}
	return result;
}


/*
 * Returns the prime factorization as a list of factor-power pairs, from the given factor list. The given list must be in ascending order.
 * Examples:
 *   toFactorPowerList([2, 2, 2]) = [[2, 3]]
 *   toFactorPowerList([3, 5]) = [[3, 1], [5, 1]]
 */
function toFactorPowerList(factors) {
	var result = [];
	var factor = factors[0];
	var count = 1;
	for (var i = 1; i < factors.length; i++) {
		if (factors[i] == factor) {
			count++;
		} else {
			result.push([factor, count]);
			factor = factors[i];
			count = 1;
		}
	}
	result.push([factor, count]);
	return result;
}