let printN = (maxN) => {
   let nextVal = (x,n) => { 
    let b2 = new Big(2);
    let val = b2.pow(n).mul(3).mul(b2.minus(x).sqrt());
    console.log(val.toString()); 
    return x.plus(2).sqrt(); 
  };

  let s = (new Big(3)).sqrt().plus(2).sqrt();
  for (let n=2; n<maxN; n++) { 
    Big.DP = n + 10;  
    s = nextVal(s,n); }
  };
  printN(500);

[2] Try on JSFiddle: https://jsfiddle.net/asgxL84y/

[3] The math: https://pasteboard.co/JeNGeB0.png