Example IFSharp notebook that intellisense does not work.

IntellisenseError.ipynb

{
 "metadata": {
  "language": "fsharp",
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###Multiples of 3 and 5\n",
      "####Problem 1  \n",
      "If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.\n",
      "\n",
      "Find the sum of all the multiples of 3 or 5 below 1000."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "[1..999] |> List.filter(fun x -> x%3=0||x%5=0) |> List.sum"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "val it : int * float = (233168, 0.0016092)"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###Even Fibonacci numbers\n",
      "####Problem 2 \n",
      "Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:\n",
      "\n",
      "1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...\n",
      "\n",
      "By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "let fibs = (1,2) |> Seq.unfold (fun (a,b) -> Some(a,(b,b+a)))\n",
      "fibs |> Seq.takeWhile (fun n -> n < 4000000)\n",
      "     |> Seq.filter (fun n -> n%2=0)\n",
      "     |> Seq.sum"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "val it : int * float = (4613732, 0.0100563)"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###Largest prime factor\n",
      "####Problem 3\n",
      "The prime factors of 13195 are 5, 7, 13 and 29.\n",
      "\n",
      "What is the largest prime factor of the number 600851475143 ?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "let rec factor n =       \n",
      "    {2L .. int64(sqrt(float n))} \n",
      "    |> Seq.tryFind (fun k -> n%k=0L)\n",
      "    |> function\n",
      "       |Some k -> k :: factor (n/k)\n",
      "       |None -> [n]\n",
      "\n",
      "factor 600851475143L |> List.max"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "val it : int64 = 6857L"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###Largest palindrome product\n",
      "####Problem 4\n",
      "A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 \u00d7 99.\n",
      "\n",
      "Find the largest palindrome made from the product of two 3-digit numbers."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "let isPalindrome n = \n",
      "    let s = (string n).ToCharArray() in Array.rev s = s\n",
      "\n",
      "// assuming the range of answers is 900 to 999\n",
      "\n",
      "seq [ for a in 900 .. 999 do\n",
      "        for b in 900 .. a do\n",
      "            if isPalindrome(a*b) then\n",
      "                    yield a*b ]\n",
      "|> Seq.max"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "val it : int = 906609"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###Smallest multiple\n",
      "####Problem 5\n",
      "2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.\n",
      "\n",
      "What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "/// greatest common divisor\n",
      "let rec gcd a b = if b = 0L then a else gcd b (a%b)\n",
      "/// least common multiple\n",
      "let lcm a b = a * b / gcd a b\n",
      "\n",
      "[1L .. 20L] |> List.reduce lcm"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "val it : int64 = 232792560L"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###Sum square difference\n",
      "####Problem 6\n",
      "The sum of the squares of the first ten natural numbers is,\n",
      "\n",
      "$1^2 + 2^2 + ... + 10^2 = 385$  \n",
      "The square of the sum of the first ten natural numbers is,\n",
      "\n",
      "$(1 + 2 + ... + 10)^2 = 55^2 = 3025$  \n",
      "Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is $3025 \u2212 385 = 2640$.\n",
      "\n",
      "Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "let sqr x = x*x\n",
      "([1..100] |> List.sum |> sqr) - ([1..100] |> List.sumBy sqr)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "val it : int = 25164150"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###10001st prime\n",
      "####Problem 7\n",
      "By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.\n",
      "\n",
      "What is the 10 001st prime number?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "let isPrime n =\n",
      "    let isqrt x = int(sqrt(float x))\n",
      "    {2 .. isqrt n} |> Seq.exists (fun i -> n%i=0) |> not\n",
      "\n",
      "// assuming that the 10001st prime is less than 1M\n",
      "{2 .. 1000000}\n",
      "|> Seq.filter isPrime\n",
      "|> Seq.nth 10000  // F# indices start at 0"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "val it : int = 104743"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###Largest product in a series\n",
      "####Problem 8\n",
      "Find the greatest product of five consecutive digits in the 1000-digit number."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "open System.IO\n",
      "\n",
      "let file = __SOURCE_DIRECTORY__ + \"/txt/p008.txt\"\n",
      "\n",
      "File.ReadAllLines(file)\n",
      "|> Array.reduce (+)\n",
      "|> fun n -> n.ToCharArray()\n",
      "|> Seq.windowed 5\n",
      "|> Seq.map (fun s -> s |> Array.map(string >> int)\n",
      "                       |> Array.reduce ( * ))\n",
      "|> Seq.max"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "val it : int = 40824"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###Special Pythagorean triplet\n",
      "####Problem 9\n",
      "A Pythagorean triplet is a set of three natural numbers, $a < b < c$, for which,\n",
      "\n",
      "$a^2 + b^2 = c^2$  \n",
      "For example, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$.\n",
      "\n",
      "There exists exactly one Pythagorean triplet for which $a + b + c = 1000$.\n",
      "Find the product $abc$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "let isTriplet a b c = a*a+b*b=c*c\n",
      "seq [ for a = 1 to 1000 do\n",
      "        for b = 1 to a do\n",
      "          if isTriplet a b (1000-a-b) then\n",
      "            yield a*b*(1000-a-b) ]\n",
      "|> Seq.head"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 115,
       "text": [
        "val it : int = 31875000"
       ]
      }
     ],
     "prompt_number": 115
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "###Summation of primes\n",
      "###Problem 10\n",
      "The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\n",
      "\n",
      "Find the sum of all the primes below two million."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "// prime sieve that generates primes under a given number\n",
      "let getPrimes n = \n",
      "    let p = Array.create (n+1) true\n",
      "    for i = 2 to int(sqrt(float n)) do\n",
      "        if p.[i] then\n",
      "            for k = 2 to n/i do\n",
      "                p.[k*i] <- false\n",
      "    [ for i = 2 to n do\n",
      "        if p.[i] then yield i ]\n",
      "\n",
      "getPrimes 2000000\n",
      "|> List.sumBy int64"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "val it : int64 = 142913828922L"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "// intellisense does not work here\n",
      "open System"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}