### 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

### Integer Right Triangles (Project Euler Problem 39)

Poblem

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p ≤ 1000, is the number of solutions maximised?

Solution

``````
open System

let buildArrays xs ys zs limits = seq{
for x in xs do
for y in ys do
if x < y then
for z in zs do
if (x*x + y*y = z*z) then
for limit in limits do
if (x + y + z = limit) then
yield limit, x, y, z}

let First (a,b,c,d) = a

let pyhtosArrays = buildArrays [1..999] [1..999] [1..999] [1..999]
|> Seq.toList
|> List.map (fun x -> First x)

let results = pyhtosArrays |> Seq.countBy id
|> Seq.toList
|> List.sortByDescending snd

``````

### 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.