--description--

The number 7 is special, because 7 is 111 written in base 2, and 11 written in base 6 (i.e. $7_{10} = {11}_6 = {111}_2$). In other words, 7 is a repunit in at least two bases $b > 1$.

We shall call a positive integer with this property a strong repunit. It can be verified that there are 8 strong repunits below 50: {1, 7, 13, 15, 21, 31, 40, 43}. Furthermore, the sum of all strong repunits below 1000 equals 15864.

Find the sum of all strong repunits below ${10}^{12}$.

--hints--

strongRepunits() should return 336108797689259260.

assert.strictEqual(strongRepunits(), 336108797689259260);

--seed--

--seed-contents--

function strongRepunits() {

  return true;
}

strongRepunits();

--solutions--

// solution required