2011-08-13 infinite-sequence-of-primes-by-sequence-expressions

# Title: Infinite sequence of primes
# Author: Mikael Lundin
# Link: http://blog.mikaellundin.name/2011/08/13/infinite-sequence-of-primes-by-sequence-expressions.html

isPrime.fs

let isPrime number primes =
  let sqrtn = float >> sqrt >> int
  primes
   |> Seq.takeWhile (fun n -> n <= (sqrtn number))
   |> Seq.exists (fun n -> number % n = 0)
 |> not

primes.fs

let rec primes = 
  let isPrime number primes =
    let sqrtn = float >> sqrt >> int
    primes
     |> Seq.takeWhile (fun n -> n <= (sqrtn number))
     |> Seq.exists (fun n -> number % n = 0)
   |> not
 
  let rec primes' current =
    seq {
     if primes |> isPrime current then
     yield current
   yield! primes' (current + 2)
    }
  seq {
    yield 2
    yield! primes' 3
  } |> Seq.cache

primesPrime.fs

let rec primes' current =
  seq {
   if primes |> isPrime current then
   yield current
 yield! primes' (current + 2)
  }

seq1.fs

seq { 
  yield 0
  yield! [1; 2; 3]
  yield! [4; 5; 6]
  yield! [7; 8; 9]
}

seq2.fs

let rec alternating = 
  seq {
    yield true
    yield false
    yield! alternating
  }

seq3.fs

seq {
  yield 2
  yield! primes' 3
} |> Seq.cache