chore(i8n,learn): processed translations

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---
id: 5900f4f31000cf542c510006
title: 问题391跳跃游戏
title: 'Problem 391: Hopping Game'
challengeType: 5
videoUrl: ''
forumTopicId: 302056
dashedName: problem-391-hopping-game
---
# --description--
当将数字从0写入k到二进制时令sk为1的数。例如以二进制形式写0到5我们有0,1,10,11,100,101。有7个1所以s5 = 7.序列S = {skk≥0}开始{0,1 2,4,5,7,9,12......}。
Let sk be the number of 1s when writing the numbers from 0 to k in binary.
一个游戏由两个玩家玩。在游戏开始之前选择数字n。计数器c从0开始。每转一圈玩家选择一个从1到n的数字然后用该数字增加c。结果值c必须是S的成员。如果没有更多有效的移动则玩家输掉。
For example, writing 0 to 5 in binary, we have 0, 1, 10, 11, 100, 101. There are seven 1s, so s5 = 7.
例如设n = 5.c从0开始。玩家1选择4所以c变为0 + 4 = 4.玩家2选择5所以c变为4 + 5 = 9.玩家1选择3所以c变为9 + 3 = 12.等等。请注意c必须始终属于S并且每个玩家最多可以将c增加n。
The sequence S = {sk : k ≥ 0} starts {0, 1, 2, 4, 5, 7, 9, 12, ...}.
设Mn是第一个玩家在第一个回合强制获胜时可以选择的最高数字如果没有这样的移动则Mn= 0。例如M2= 2M7= 1且M20= 4。
A game is played by two players. Before the game starts, a number n is chosen. A counter c starts at 0. At each turn, the player chooses a number from 1 to n (inclusive) and increases c by that number. The resulting value of c must be a member of S. If there are no more valid moves, the player loses.
给定ΣMn3 = 81501≤n≤20。
For example: Let n = 5. c starts at 0. Player 1 chooses 4, so c becomes 0 + 4 = 4. Player 2 chooses 5, so c becomes 4 + 5 = 9. Player 1 chooses 3, so c becomes 9 + 3 = 12. etc. Note that c must always belong to S, and each player can increase c by at most n.
找ΣMn3表示1≤n≤1000。
Let M(n) be the highest number the first player can choose at her first turn to force a win, and M(n) = 0 if there is no such move. For example, M(2) = 2, M(7) = 1 and M(20) = 4.
Given Σ(M(n))3 = 8150 for 1 ≤ n ≤ 20.
Find Σ(M(n))3 for 1 ≤ n ≤ 1000.
# --hints--
`euler391()`应该返回61029882288
`euler391()` should return 61029882288.
```js
assert.strictEqual(euler391(), 61029882288);