The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, … By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form …
The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form 26972593−1; it contains exactly 2,098,960 digits. Subsequently other Mersenne primes, of the form 2p−1, have been found which contain more digits. However, in 2004 there was found a …
A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before. For example, 44 → 32 → 13 → 10 → 1 → 1 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 …
A googol (10100) is a massive number: one followed by one-hundred zeros; 100100 is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1. Considering natural numbers of the form, ab, where a, b < 100, what is the maximum digital sum? …
This program generates 25 polynomials of increasing degree randomly using a Mersenne twister, solves them via Horner’s rule and records runtime. /////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <vector> #include <random> #include <iomanip> #include <chrono> /////////////////////////////////////////////////////////////////////////////// std::vector<int> randIntGen(int count); float randRealGen(void); void polyPrint(float x, std::vector<int> polyVals); void hornersRuleTime(float x, int n, std::vector<int> polyVals); …
The bot doesn’t do much but tell fortunes, give a pong response to a ping, and log the chatroom. Will probably add to is as I get bored. The fortunes text file can be found here if interested. import socket import random from config import * def processChat(sock, buff): buff = buff.strip() …
Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5: 22=4, 23=8, 24=16, 25=32 32=9, 33=27, 34=81, 35=243 42=16, 43=64, 44=256, 45=1024 52=25, 53=125, 54=625, 55=3125 If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms: 4, …
/////////////////////////////////////////////////////////////////////////////// // This program takes a RSA encrypted message in a text file, // by given parameters, and decrypts it. After which it outputs to console. /////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <fstream> #include <sstream> #include <vector> #include <math.h> /////////////////////////////////////////////////////////////////////////////// void fileRead(std::ifstream &inFile, std::vector &fileBuff); void decrypt(std::vector<int> cipherText, std::vector<char> &plaintText, int pq, …
This program takes an input WAM, and applies Kruskal’s and Prim’s algorithms to it. /////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <vector> #include <sstream> /////////////////////////////////////////////////////////////////////////////// struct Edge { int vertOne, vertTwo, weight; Edge(int one, int two, int passedWeight) { this->vertOne = one; this->vertTwo = two; this->weight = passedWeight; } }; class Vertex { …
Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420. We shall call a positive integer …