--description--

A positive integer with $k$ (decimal) digits is called balanced if its first $⌈\frac{k}{2}⌉$ digits sum to the same value as its last $⌈\frac{k}{2}⌉$ digits, where $⌈x⌉$, pronounced ceiling of $x$, is the smallest integer $≥ x$, thus $⌈π⌉ = 4$ and $⌈5⌉ = 5$.

So, for example, all palindromes are balanced, as is 13722.

Let $T(n)$ be the sum of all balanced numbers less than $10^n$.

Thus: $T(1) = 45$, $T(2) = 540$ and $T(5) = 334\,795\,890$.

Find $T(47)\,mod\,3^{15}$

--hints--

balancedNumbers() should return 6273134.

assert.strictEqual(balancedNumbers(), 6273134);

--seed--

--seed-contents--

function balancedNumbers() {

  return true;
}

balancedNumbers();

--solutions--

// solution required