steloflute

http://projecteuler.net/problem=65 Problem 65 12 March 2004 The square root of 2 can be written as an infinite continued fraction. 2 = 1 + 1 2 + 1 2 + 1 2 + 1 2 + ... The infinite continued fraction can be written, 2 = [1;(2)], (2) indicates that 2 repeats ad infinitum. In a similar way, 23 = [4;(1,3,1,8)].It turns out that the sequence of partial values of continued fractions for square roots p..

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http://projecteuler.net/problem=64 Problem 64 27 February 2004 All square roots are periodic when written as continued fractions and can be written in the form: N = a0 + 1 a1 + 1 a2 + 1 a3 + ... For example, let us consider 23: 23 = 4 + 23 — 4 = 4 + 1 = 4 + 1 1 23—4 1 + 23 – 3 7 If we continue we would get the following expansion: 23 = 4 + 1 1 + 1 3 + 1 1 + 1 8 + ... The process can be summarise..

http://projecteuler.net/problem=63 Problem 63 13 February 2004 The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power.How many n-digit positive integers exist which are also an nth power? Answer: 49 * Racket #lang racket (define (digits n) (add1 (floor (/ (log n) (log 10))))) (define sum 0) (define d 1) (for* ([n (in-range 1 10)] [d (in..

http://projecteuler.net/problem=62 Problem 62 30 January 2004 The cube, 41063625 (3453), can be permuted to produce two other cubes: 56623104 (3843) and 66430125 (4053). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.Find the smallest cube for which exactly five permutations of its digits are cube. Answer: 127035954683 * Racket #lang..

#lang racket (require racket/generator) (define (permute v) (generator () (define count 0) (define len (vector-length v)) (define sorted (sort (vector->list v) level (sub1 len)) (begin (set! count (add1 count)) (yield v)) (for ([i sorted]) (unless (for/or ([priorLevel (in-range 0 level)]) (= i (vector-ref v priorLevel))) (vector-set! v level i) (loop (add1 level)))))))) (define (permutations v) ..

http://prog21.dadgum.com/154.html Do You Really Want to be Doing this When You're 50?When I was still a professional programmer, my office-mate once asked out of the blue, "Do you really want to be doing this kind of work when you're fifty?" I have to say that made me stop and think. To me, there's an innate frustration in programming. It doesn't stem from having to work out the solutions to dif..

http://projecteuler.net/problem=61Problem 61 16 January 2004 Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae: Triangle P3,n=n(n+1)/2 1, 3, 6, 10, 15, ... Square P4,n=n2 1, 4, 9, 16, 25, ... Pentagonal P5,n=n(3n1)/2 1, 5, 12, 22, 35, ... Hexagonal P6,n=n(2n1) 1, 6, 15, 28, 45, ... Heptagona..

http://www.cse.wustl.edu/~loui/praiseieee.html draft under submission; copyright reserved by author In Praise of Scripting: Real Programming Pragmatism Ronald P. Loui Associate Professor of CSE Washington University in St. Louis ABSTRACT: This article's main purpose is to review the changes in programming practices known collectively as the "rise of scripting," as predicted in 1998 IEEE COMPUTER..

http://www.newlisp.org/ newLISP is a Lisp-like, general-purpose scripting language. It is especially well-suited for applications in AI, web search, natural language processing, machine learning and statistics. Because of its small resource requirements, newLISP is also excellent for embedded systems applications. Most of the functions you will ever need are already built in. This includes netwo..