The powers of Phi conjugated into whole numbers also converge to Phi

Rephiprocal Raphio

// For any even integer n: 
// Phi^n + 1/Phi^n = a whole number
// For any odd integer n:
// Phi n  –  1 / Phi n = a whole number
// goldennumber.net/powers-of-phi

function Rephiprocal(x,n){
    var P = .5+Math.sqrt(5)/2,
        R=Math.pow(P,n); 
    return R + Math.pow(-1,n)/R;
}

// Array.reduce functor
function Raphio(array, next){
    var last = array[array.length-1];
    console.info(next +'/'+ last, next/last);
  return [last/next, next]
}

//@return an array with digits from 0 to n
function Gen(n){
    return (new Array(n)).join().split(',');
}

if ('run')
    Gen(511)
        .map(Rephiprocal)
        .reduce(Raphio, [1])