How to find elements in array JavaScript where array[i] = i?

Question

I need to find elements in an array of numbers where arr[i] === i, meaning the element must be equal to the array index.
They must be found with using recursion, not just by cycle.
I would be very thankful, if someone help, because I've spent many hours and can't do anything.
I've tried to use Binary Search but it doesn't work. In the end I've got only the empty array.

function fixedPointSearch(arr, low, high) {

  let middle = Math.floor((high - low) / 2);
  
  console.log(  low, high, middle )
  
  let arrRes = [];
  if (arr[middle] === middle)
    { arrRes.push(arr[middle]); }
  else if (arr[middle] > middle)
    { fixedPointSearch(arr, middle + 1, high); }
  else
    { fixedPointSearch(arr, low, middle - 1); }

  return arrRes;
}
const arr1 = [-10, -3, 2, 3, 6, 7, 8, 9, 10, 12, 16, 17];
console.log(fixedPointSearch(arr1, 0, arr1.length - 1));

Answer 1

You can solve this w/o additional temporary arrays and parameters, by simply shortening the array in each step:

const myArray = [0, 5, 2, 4, 7, 9, 6];

function fixedPointSearch(arrayToTest) {
  if (arrayToTest.length === 0) {
    return [];
  }

  const lastIndex = arrayToTest.length - 1;
  const lastItem = arrayToTest[lastIndex];
  const remainingItems = arrayToTest.slice(0, lastIndex);

  return lastItem === lastIndex
    ? [...fixedPointSearch(remainingItems), lastItem]
    : fixedPointSearch(remainingItems);
}

console.log(fixedPointSearch(myArray));