a-conjecture-of-mine

 // This script is a simple test for the following conjecture:
 
 // Let S: N -> N be the sum of the digits of a positive integer.
 // For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an interger.
 
 function sumDigits(n) {
     let parc = Math.abs(n), sum = 0;
 
     while (parc > 0) {
         sum += parc % 10;
         parc = Math.floor(parc / 10);
     }
 
     return sum;
 }
 
 function getSums(max) {
     return Array.from({length: 2 * max}, (_, i) => sumDigits(i));
 }
 
 export function counterexempl(max) {
     const sums = getSums(max);
 
     for (let a = 1; a <= max; a++)
         for (let b = a; b <= max; b++) {
             const diff = sums[a + b] - sums[a] - sums[b];
             if (diff % 9 !== 0) return true;
         }
 
     return false;
 }