### Microsoft Azure Notebooks - Live code - F#, R, and Python

I was exploring Jupyter notebooks , that combines live code, markdown and data, through Microsoft's implementation, known as MS Azure Notebooks , putting together a small library of R and F# notebooks . As Microsoft's FAQ for the service describes it as : ...a multi-lingual REPL on steroids. This is a free service that provides Jupyter notebooks along with supporting packages for R, Python and F# as a service. This means you can just login and get going since no installation/setup is necessary. Typical usage includes schools/instruction, giving webinars, learning languages, sharing ideas, etc. Feel free to clone and comment... In R Azure Workbook for R - Memoisation and Vectorization Charting Correlation Matrices in R In F# Charnownes Constant in FSharp.ipynb Project Euler - Problems 18 and 67 - FSharp using Dynamic Programming

### Digit cancelling fractions (Project Euler Problem 33)

Problem

The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.

We shall consider fractions like, 30/50 = 3/5, to be trivial examples.

There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator. If the product of these four fractions is given in its lowest common terms, find the value of the denominator.

(link to Problem 33 on the Project Euler site)

Note

This is a somewhat crude solution, since I am only just getting back into solving these problems, or working with F#, but there are several similar problems for which I can develop properly factored, reusable functions.

Solution

``````
open System

let product xs ys = seq{for x in xs do
for y in ys do
let a = float x % float 10
let b = System.Math.Floor(float y / float 10)
let c = (float x - a) / float 10
let d = float y - (b * float 10)
if a = b && x < y && (c/d = float x / float y) then
yield x, y}

let fstList = product [11..99] [11..99] |> Seq.toList |> List.map (fun x -> fst x)
let sndList = product [11..99] [11..99] |> Seq.toList |> List.map (fun x -> snd x)

let fstProd = fstList.[0] * fstList.[1] * fstList.[2] * fstList.[3]
let sndProd = sndList.[0] * sndList.[1] * sndList.[2] * sndList.[3]

let result = float fstProd / float sndProd
```
```

### Microsoft Azure Notebooks - Live code - F#, R, and Python

I was exploring Jupyter notebooks , that combines live code, markdown and data, through Microsoft's implementation, known as MS Azure Notebooks , putting together a small library of R and F# notebooks . As Microsoft's FAQ for the service describes it as : ...a multi-lingual REPL on steroids. This is a free service that provides Jupyter notebooks along with supporting packages for R, Python and F# as a service. This means you can just login and get going since no installation/setup is necessary. Typical usage includes schools/instruction, giving webinars, learning languages, sharing ideas, etc. Feel free to clone and comment... In R Azure Workbook for R - Memoisation and Vectorization Charting Correlation Matrices in R In F# Charnownes Constant in FSharp.ipynb Project Euler - Problems 18 and 67 - FSharp using Dynamic Programming

### Consecutive Prime Sum (Project Euler - Problem 50)

Problem The prime 41, can be written as the sum of six consecutive primes: 41 = 2 + 3 + 5 + 7 + 11 + 13 This is the longest sum of consecutive primes that adds to a prime below one-hundred. The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953. Which prime, below one-million, can be written as the sum of the most consecutive primes? Note Some libraries used in this code are F# modules I use, but have also published as a  Nuget library , such as EulerLib.GetPrimes() and  EulerLib. isPrime(). You need to reference the NuGetLibrary to use this code as is. Solution #load "Stat.fs" #load "Print.fs" #load "EulerLib.fs" open Stat open Print open EulerLib open System let rec FindLongestPrimeSequenceSum (primeList:list ) (nextItem:int) lessThanValue (primeArray:list ) bestPrime (correctArray:list )

### First Post and Raison d'Etre

I am enjoying delving into learning F#, currently working through Programming F#: A comprehensive guide for writing simple code to solve complex problems on mu iPad via Kindle, as well as using a variety of web sources: WikiBook's F# Programming Project Euler, a "series of challenging mathematical/computer programming problems" F# News Inside F# Learn Visual F# (MSDN) I am currently working with MS Visual Studio Shell 2010 and F# 2.0 to work though various self-designed ideas, as well as working through various problems from Project Euler.