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---
id: 5900f3fa1000cf542c50ff0c
title: '问题 140改进的斐波那契金块'
challengeType: 5
forumTopicId: 301769
dashedName: problem-140-modified-fibonacci-golden-nuggets
---
# --description--
考虑无穷级数 $A_G(x) = xG_1 + x^2G_2 + x^3G_3 + \cdots$,其中 $G_k$ 是二阶递归关系的第 $k$ 项,$G_k = G_{k 1} + G_{k 2}, G_1 = 1$,且 $G_2 = 4$;该数列为 $1, 4, 5, 9, 14, 23, \ldots$。
在这个问题中,我们关注的是那些使得 $A_G(x)$ 为正整数的 $x$ 的值。
前五个对应的自然数 $x$ 如下。
| $x$ | $A_G(x)$ |
| ----------------------------- | -------- |
| $\frac{\sqrt{5} 1}{4}$ | $1$ |
| $\frac{2}{5}$ | $2$ |
| $\frac{\sqrt{22} 2}{6}$ | $3$ |
| $\frac{\sqrt{137} 5}{14}$ | $4$ |
| $\frac{1}{2}$ | $5$ |
当 $x$ 是有理数时,我们称 $A_G(x)$ 是一个金砖,因为这样的数字逐渐变得稀少;例如,第 20 个金砖是 211345365。 请计算出前三十个金砖之和。
# --hints--
`modifiedGoldenNuggets()` 应该返回 `5673835352990`
```js
assert.strictEqual(modifiedGoldenNuggets(), 5673835352990);
```
# --seed--
## --seed-contents--
```js
function modifiedGoldenNuggets() {
return true;
}
modifiedGoldenNuggets();
```
# --solutions--
```js
// solution required
```