Sudal's Garage

Question: Euler discovered the remarkable quadratic formula:n2+n+41It turns out that the formula will produce 40 primes for the consecutive integer values 0≤n≤39. However, when n=40,40^2+40+41=40(40+1)+41 is divisible by 41, and certainly when n=41,41^2+41+41 is clearly divisible by 41. The incredible formula n^2−79n+1601 was discovered, which produces 80 primes for the consecutive values 0≤n≤79..

Question: The Fibonacci sequence is defined by the recurrence relation:Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.Hence the first 12 terms will be:F1 = 1 F2 = 1 F3 = 2 F4 = 3 F5 = 5 F6 = 8 F7 = 13 F8 = 21 F9 = 34 F10 = 55 F11 = 89 F12 = 144The 12th term, F12, is the first term to contain three digits.What is the index of the first term in the Fibonacci sequence to contain 1000 digits? 문제: 피보나치 수열..

Question: A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:012 021 102 120 201 210What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 ..

Question: A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.A number n is called deficient if the sum of its proper divisors is less than n and it is called abundant if this sum exceeds n.As 12 is the smallest abundant num..

Question: Using names.txt (right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score.For example, when the list is sorted into alphabetical order, COLIN, which is worth 3..