五十五.吕克雷尔数(Lychrel numbers) 如果我们把\(47\)翻转过来并和其自身相加,结果是\(47+74=121\)是一个回文数.并不是所有的数都可以这么快的变成回文数,比如说: \[ \begin{aligned}349 + 943 &= 1292\\1292 + 2921 &= 4213\\4213 + 3124 &= 7337\end{aligned} \] 也就是说349用了三次迭代才变成一个回文数. 尽管现在还没有人能够证明,但是普遍认为有些数字,比如说1…

If we take 47, reverse and add, 47 + 74 = 121, which is palindromic. Not all numbers produce palindromes so quickly. For example, 349 + 943 = 1292, 1292 + 2921 = 4213 4213 + 3124 = 7337 That is, 349 took three iterations to arrive at a palindrome. Al…

A natural number, N, that can be written as the sum and product of a given set of at least two natural numbers, {a1, a2, ... , ak} is called a product-sum number: N = a1 + a2 + ... + ak = a1 × a2 × ... × ak. For example, 6 = 1 + 2 + 3 = 1 × 2 × 3. Fo…

先说最暴力的算法,直接对一万内的每个数字暴力分解因子(对每个数字的时间复杂度是O(sqrt(n)的),然后,用个数组记录下来因子和,然后寻找 亲密数. 好一点:要先打个素数表,然后对每个数字,分解素因子, 假设因子和函数为,则, 推导后: ------>证明过程见<初等数论及其应用>(原书第六版)184-185页 有个坑就是a!=b,在这里错了好几发.... 看了下官方的题解,最终用的方法就是我图片里的那个公式. ------------->开启了支持数学公式,可是还是不支持,很蛋…

In Problem 42 we dealt with triangular problems, in Problem 44 of Project Euler we deal with pentagonal number, I can only wonder if we have to deal with septagonal numbers in Problem 46. Anyway the problem reads Pentagonal numbers are generated by t…

本题来自 Project Euler 第21题:https://projecteuler.net/problem=21 ''' Project Euler: Problem 21: Amicable numbers Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a ≠ b…

本题来自 Project Euler 第12题:https://projecteuler.net/problem=12 # Project Euler: Problem 12: Highly divisible triangular number # The sequence of triangle numbers is generated by adding the natural numbers. # So the 7th triangle number would be 1 + 2 + 3…

本题来自 Project Euler 第11题:https://projecteuler.net/problem=11 # Project Euler: Problem 10: Largest product in a grid # In the 20×20 grid below, four numbers along a diagonal line have been marked in red. # The product of these numbers is 26 × 63 × 78 ×…

上一次接触 project euler 还是2011年的事情,做了前三道题,后来被第四题卡住了,前面几题的代码也没有保留下来. 今天试着暴力破解了一下,代码如下: (我大概是第 172,719 个解出这道题的人) program 4 A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.…

开始做 Project Euler 的练习题.网站上总共有565题,真是个大题库啊! # Project Euler, Problem 1: Multiples of 3 and 5 # If we list all the natural numbers below 10 # that are multiples of 3 or 5, we get 3, 5, 6 and 9. # The sum of these multiples is 23. # Find the sum of all…