This problem was presented to me: given a list of numbers, 1-1000, can you name the smallest base in which each one is a palindrome?

any_base_palindromes.js

var palindrome_test = function(array) {
  for (var i = 0; i <= array.length - 1; i++) {
    if (array[i] !== array[array.length - i - 1]) {
      return false;
    }
  }
  return true;
}

var int2base = function(int, base) {
  if (int === 0 || base === 0) {
    return [0];
  }
  if (base == 1) {
    // this really is the easiest way to fill an array with numbers in vanilla js
    return Array.apply(null, Array(int)).map(Number.prototype.valueOf,1);
  }
  var digits = [];
  while (int) {
    digits.unshift(int % base);
    int = Math.floor(int/base);
  }
  return digits;
}

// nested loops, oh no... probably a better way...
for (var i = 1; i <= 1000; i++) {
  for (var j = 2; j <= i + 1; j++) {
    if (palindrome_test(int2base(i, j))) {
      // console.log(int2base(i, j));
      console.log(i + " is a palindrome in base " + j);
      break;
    }
  }
}

Or even better: compare:
arr.slice(0, Math.ceil(arr.length/2))
arr.slice(Math.floor(arr.length/2), arr.length)