Woodall Primes

Woodall Primes are prime numbers that are also Woodall number.

Find the Woodall prime numbers less than N

Given a number N, print all Woodall primes smaller than or equal to N. 
Examples:

Input: N = 10 
Output: 7
Input: N = 500 
Output: 7, 23, 383 

Approach: The idea is to use Sieve of Eratosthenes to check that a number is prime or not efficiently. Then, Iterate over integers from 1 to N, and for every number check that if it is prime or not and it is Woodall number or not. If a number is prime also a Woodall number, Then it a Woodall prime.

Below is the implementation of above algorithm:

C++

// C++ implementation to print all Woodall
// primes smaller than or equal to n.
#include <bits/stdc++.h>
using namespace std;

// Function to check if a number
// N is Woodall
bool isWoodall(int x)
{
  // If number is even, return false.
  if (x % 2 == 0)
    return false;

  // If x is 1, return true.
  if (x == 1)
    return true;

  x = x + 1; // Add 1 to make x even

  // While x is divisible by 2
  int p = 0;
  while (x % 2 == 0) {
    // Divide x by 2
    x = x / 2;

    // Count the power
    p = p + 1;

    // If at any point power and
    // x became equal, return true.
    if (p == x)
      return true;
  }

  return false;
}

// Function to generate all primes and checking
// whether number is Woodall or not
void printWoodallPrimesLessThanN(int n)
{
  // Create a boolean array "prime[0..n]" and
  // initialize all entries it as true. A value
  // in prime[i] will finally be false if i is
  // Not a prime, else true.
  vector<bool> prime(n + 1, true);

  int p = 2;
  while (p * p <= n) {
    // If prime[p] is not changed,
    // then it is a prime
    if (prime[p])

      // Update all multiples of p
      for (int i = p * 2; i <= n; i += p)
        prime[i] = false;
    p += 1;
  }

  // Print all Woodall prime numbers
  for (p = 2; p <= n; p++) {

    // checking whether the given number
    // is prime Woodall or not
    if (prime[p] && isWoodall(p))
      cout << p << " ";
  }
}

// Driver Code
int main()
{
  int n = 1000;
  printWoodallPrimesLessThanN(n);
}

// This code is contributed by phasing17

Java

// Java implementation to print all Woodall
// primes smaller than or equal to n.
import java.io.*;
import java.util.*;

class GFG
{

  // Function to check if a number
  // N is Woodall
  static Boolean isWoodall(int x)
  {

    // If number is even, return false.
    if (x % 2 == 0)
      return false;

    // If x is 1, return true.
    if (x == 1)
      return true;

    x = x + 1; // Add 1 to make x even

    // While x is divisible by 2
    int p = 0;
    while (x % 2 == 0)
    {

      // Divide x by 2
      x = x / 2;

      // Count the power
      p = p + 1;

      // If at any point power and
      // x became equal, return true.
      if (p == x)
        return true;
    }

    return false;
  }

  // Function to generate all primes and checking
  // whether number is Woodall or not
  static void printWoodallPrimesLessThanN(int n)
  {

    // Create a boolean array "prime[0..n]" and
    // initialize all entries it as true. A value
    // in prime[i] will finally be false if i is
    // Not a prime, else true.
    ArrayList<Boolean> prime = new ArrayList<Boolean>();

    for (int i = 0; i <= n; i++)
      prime.add(true);

    int p = 2;
    while (p * p <= n)
    {

      // If prime[p] is not changed,
      // then it is a prime
      if (prime.get(p))

        // Update all multiples of p
        for (int i = p * 2; i <= n; i += p)
          prime.set(i,false);
      p += 1;
    }

    // Print all Woodall prime numbers
    for (p = 2; p <= n; p++) {

      // checking whether the given number
      // is prime Woodall or not
      if (prime.get(p) && isWoodall(p))
        System.out.print(p + " ");
    }
  }

  // Driver Code
  public static void main (String []args)
  {
    int n = 1000;
    printWoodallPrimesLessThanN(n);
  }
}

// This code is contributed by Pushpesh Raj

Python3

# Python3 implementation to print all Woodall
# primes smaller than or equal to n.

# Function to check if a number
# N is Woodall
def isWoodall(x) :

    # If number is even, return false.
    if (x % 2 == 0) :
        return False

    # If x is 1, return true.
    if (x == 1) :
        return True

    x = x + 1  # Add 1 to make x even

    # While x is divisible by 2
    p = 0
    while (x % 2 == 0) :

        # Divide x by 2
        x = x / 2

        # Count the power
        p = p + 1

        # If at any point power and
        # x became equal, return true.
        if (p == x) :
            return True

    return False

# Function to generate all primes and checking
# whether number is Woodall or not
def printWoodallPrimesLessThanN(n):

    # Create a boolean array "prime[0..n]" and
    # initialize all entries it as true. A value
    # in prime[i] will finally be false if i is
    # Not a prime, else true.
    prime = [True] * (n + 1);
    p = 2;
    while (p * p <= n):

        # If prime[p] is not changed,
        # then it is a prime
        if (prime[p]):

            # Update all multiples of p
            for i in range(p * 2, n + 1, p):
                prime[i] = False;
        p += 1;

    # Print all Woodall prime numbers
    for p in range(2, n + 1):

        # checking whether the given number
        # is prime Woodall or not
        if (prime[p] and isWoodall(p)):
            print(p, end = " ");

# Driver Code
n = 1000;
printWoodallPrimesLessThanN(n)

C#

// C# implementation to print all Woodall
// primes smaller than or equal to n.
using System;
using System.Collections.Generic;

class GFG
{

  // Function to check if a number
  // N is Woodall
  static bool isWoodall(int x)
  {

    // If number is even, return false.
    if (x % 2 == 0)
      return false;

    // If x is 1, return true.
    if (x == 1)
      return true;

    x = x + 1; // Add 1 to make x even

    // While x is divisible by 2
    int p = 0;
    while (x % 2 == 0)
    {

      // Divide x by 2
      x = x / 2;

      // Count the power
      p = p + 1;

      // If at any point power and
      // x became equal, return true.
      if (p == x)
        return true;
    }

    return false;
  }

  // Function to generate all primes and checking
  // whether number is Woodall or not
  static void printWoodallPrimesLessThanN(int n)
  {

    // Create a boolean array "prime[0..n]" and
    // initialize all entries it as true. A value
    // in prime[i] will finally be false if i is
    // Not a prime, else true.
    List<bool> prime = new List<bool>();
    for (int i = 0; i <= n; i++)
      prime.Add(true);


    int p = 2;
    while (p * p <= n)
    {

      // If prime[p] is not changed,
      // then it is a prime
      if (prime[p])

        // Update all multiples of p
        for (int i = p * 2; i <= n; i += p)
          prime[i] = false;
      p += 1;
    }

    // Print all Woodall prime numbers
    for (p = 2; p <= n; p++) {

      // checking whether the given number
      // is prime Woodall or not
      if (prime[p] && isWoodall(p))
        Console.Write(p + " ");
    }
  }

  // Driver Code
  public static void Main(string[] args)
  {
    int n = 1000;
    printWoodallPrimesLessThanN(n);
  }
}

// This code is contributed by phasing17

Javascript

// Python3 implementation to print all Woodall
// primes smaller than or equal to n.

// Function to check if a number
// N is Woodall
function isWoodall(x)
{
    // If number is even, return false.
    if (x % 2 == 0)
        return false

    // If x is 1, return true.
    if (x == 1)
        return true

    x = x + 1  // Add 1 to make x even

    // While x is divisible by 2
    let p = 0
    while (x % 2 == 0)
    {
        // Divide x by 2
        x = x / 2

        // Count the power
        p = p + 1

        // If at any point power and
        // x became equal, return true.
        if (p == x)
            return true
    }

    return false
}

// Function to generate all primes and checking
// whether number is Woodall or not
function printWoodallPrimesLessThanN(n)
{
    // Create a boolean array "prime[0..n]" and
    // initialize all entries it as true. A value
    // in prime[i] will finally be false if i is
    // Not a prime, else true.
    let prime = new Array(n + 1).fill(true)

    let p = 2;
    while (p * p <= n)
    {
        // If prime[p] is not changed,
        // then it is a prime
        if (prime[p])

            // Update all multiples of p
            for (var i = p * 2; i <= n; i += p)
                prime[i] = false;
        p += 1;
    }

    // Print all Woodall prime numbers
    for (p = 2; p <= n; p ++)
    {

        // checking whether the given number
        // is prime Woodall or not
        if (prime[p] && isWoodall(p))
            process.stdout.write(p + " ");
    }
}

// Driver Code
let n = 1000;
printWoodallPrimesLessThanN(n)



// This code is contributed by phasing17

Output:

7 23 383

Time Complexity: O(n*log(n))
Auxiliary Space: O(n)