--description--

Many numbers can be expressed as the sum of a square and a cube. Some of them in more than one way.

Consider the palindromic numbers that can be expressed as the sum of a square and a cube, both greater than 1, in exactly 4 different ways.

For example, 5229225 is a palindromic number and it can be expressed in exactly 4 different ways:

$$\begin{align} & {2285}^2 + {20}^3 \\ & {2223}^2 + {66}^3 \\ & {1810}^2 + {125}^3 \\ & {1197}^2 + {156}^3 \end{align}$$

Find the sum of the five smallest such palindromic numbers.

--hints--

sumOfSquareAndCube() should return 1004195061.

assert.strictEqual(sumOfSquareAndCube(), 1004195061);

--seed--

--seed-contents--

function sumOfSquareAndCube() {

  return true;
}

sumOfSquareAndCube();

--solutions--

// solution required