digitalRoot.js

/** A digital root is the recursive sum of all the digits in a number. Given n, take the sum of the digits of n. If that value has two digits, continue reducing in this way until a single-digit number is produced. This is only applicable to the natural numbers.
 * 
 *  Here's how it works (Ruby example given):
 * 
 *  digital_root(16)
 *   => 1 + 6
 *   => 7
 * 
 *  digital_root(942)
 *   => 9 + 4 + 2
 *   => 15 ...
 *   => 1 + 5
 *   => 6
 * 
 *   digital_root(132189)
 *   => 1 + 3 + 2 + 1 + 8 + 9
 *  => 24 ...
 *  => 2 + 4
 * => 6
 * 
 * digital_root(493193)
 * => 4 + 9 + 3 + 1 + 9 + 3
 * => 29 ...
 * => 2 + 9
 * => 11 ...
 * => 1 + 1
 * => 2
 */

function digital_root(n) {
  return (n - 1) % 9 + 1;
}