Program to find Nth term in the series 0, 2, 1, 3, 1, 5, 2, 7, 3,…

Given a number N. The task is to write a program to find the N-th term in the below series:

0, 2, 1, 3, 1, 5, 2, 7, 3, …

Examples:

Input: N = 5
Output: 1

Input: N = 10
Output: 11

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

When we look carefully at the series, we find that the series is a mixture of 2 series:

Terms at odd positions in the given series forms fibonacci series.
Terms at even positions in the given series forms a series of prime numbers.

Now, To solve the above-given problem, first check whether the input number N is even or odd.

If it is odd, set N=(N/2) + 1(since there are Two series running parallelly) and find the N^th fibonacci number.
If N is even, simply set N=N/2 and find Nth prime number.

Below is the implementation of above approach:

C++

// CPP program to find N-th term 
// in the series 
#include<bits/stdc++.h> 
#define MAX 1000 
using namespace std; 
  
// Function to find Nth Prime Number 
int NthPrime(int n) 
{ 
    int count = 0; 
    for (int i = 2; i <= MAX; i++) { 
        int check = 0; 
        for (int j = 2; j <= sqrt(i); j++) { 
            if (i % j == 0) { 
                check = 1; 
                break; 
            } 
        } 
        if (check == 0) 
            count++; 
  
        if (count == n) { 
            return i; 
            break; 
        } 
    } 
} 
  
// Function to find Nth Fibonacci Number 
int NthFib(int n) 
{ 
    // Declare an array to store  
    // Fibonacci numbers. 
    int f[n + 2]; 
    int i; 
  
    // 0th and 1st number of the 
    // series are 0 and 1 
    f[0] = 0; 
    f[1] = 1; 
  
    for (i = 2; i <= n; i++) { 
        f[i] = f[i - 1] + f[i - 2]; 
    } 
  
    return f[n]; 
} 
  
// Function to find N-th term 
// in the series 
void findNthTerm(int n) 
{ 
    // If n is even 
    if (n % 2 == 0) { 
        n = n / 2; 
        n = NthPrime(n); 
        cout << n << endl; 
    } 
  
    // If n is odd 
    else { 
        n = (n / 2) + 1; 
        n = NthFib(n - 1); 
        cout << n << endl; 
    } 
} 
  
// Driver code 
int main() 
{ 
    int X = 5; 
    findNthTerm(X); 
  
    X = 10; 
    findNthTerm(X); 
  
    return 0; 
} 

Java

// Java program to find N-th  
// term in the series 
class GFG  
{ 
  
static int MAX = 1000; 
  
// Function to find Nth Prime Number 
static int NthPrime(int n) 
{ 
int count = 0; 
int i; 
for (i = 2; i <= MAX; i++)  
{ 
    int check = 0; 
    for (int j = 2; j <= Math.sqrt(i); j++) 
    { 
        if (i % j == 0)  
        { 
            check = 1; 
            break; 
        } 
    } 
    if (check == 0) 
        count++; 
  
    if (count == n)  
    { 
        return i; 
          
    } 
} 
    return 0; 
} 
  
// Function to find Nth Fibonacci Number 
static int NthFib(int n) 
{ 
// Declare an array to store  
// Fibonacci numbers. 
int []f = new int[n + 2]; 
int i; 
  
// 0th and 1st number of the 
// series are 0 and 1 
f[0] = 0; 
f[1] = 1; 
  
for (i = 2; i <= n; i++)  
{ 
    f[i] = f[i - 1] + f[i - 2]; 
} 
  
return f[n]; 
} 
  
// Function to find N-th term 
// in the series 
static void findNthTerm(int n) 
{ 
// If n is even 
if (n % 2 == 0)  
{ 
    n = n / 2; 
    n = NthPrime(n); 
    System.out.println(n); 
} 
  
// If n is odd 
else 
{ 
    n = (n / 2) + 1; 
    n = NthFib(n - 1); 
    System.out.println(n); 
} 
} 
  
// Driver code 
public static void main(String[] args)  
{ 
    int X = 5; 
    findNthTerm(X); 
  
    X = 10; 
    findNthTerm(X); 
} 
} 
  
// This code is contributed  
// by ChitraNayal 

Python 3

# Python 3 program to find N-th  
# term in the series  
  
# import sqrt method from math module 
from math import sqrt 
  
# Globally declare constant value 
MAX = 1000
  
# Function to find Nth Prime Number 
def NthPrime(n) : 
      
    count = 0
    for i in range(2, MAX + 1) : 
          
        check = 0
        for j in range(2, int(sqrt(i)) + 1) : 
              
            if i % j == 0 : 
                check = 1
                break
  
        if check == 0 : 
            count += 1
  
        if count == n : 
            return i 
            break
  
# Function to find Nth Fibonacci Number 
def NthFib(n) : 
  
    # Create a list of size n+2 
    # to store Fibonacci numbers.  
    f = [0] * (n + 2) 
  
    # 0th and 1st number of the  
    # series are 0 and 1  
    f[0], f[1] = 0, 1
  
    for i in range(2, n + 1) : 
  
        f[i] = f[i - 1] + f[i - 2] 
  
    return f[n] 
  
# Function to find N-th  
# term in the series  
def findNthTerm(n) : 
  
    # If n is even  
    if n % 2 == 0 : 
        n //= 2
        n = NthPrime(n) 
        print(n) 
  
    # If n is odd 
    else : 
        n = (n // 2) + 1
        n = NthFib(n - 1) 
        print(n) 
  
# Driver code 
if __name__ == "__main__" : 
  
    X = 5
  
    # function calling 
    findNthTerm(X) 
  
    X = 10
    findNthTerm(X) 
      
# This code is contributed by ANKITRAI1 

C#

// C# program to find N-th term 
// in the series 
using System; 
  
class GFG  
{ 
static int MAX = 1000; 
  
// Function to find Nth Prime Number 
static int NthPrime(int n) 
{ 
int count = 0; 
int i; 
for ( i = 2; i <= MAX; i++)  
{ 
    int check = 0; 
    for (int j = 2; j <= Math.Sqrt(i); j++)  
    { 
        if (i % j == 0)  
        { 
            check = 1; 
            break; 
        } 
    } 
    if (check == 0) 
        count++; 
  
    if (count == n)  
    { 
        return i; 
    } 
} 
    return 0; 
} 
  
// Function to find Nth Fibonacci Number 
static int NthFib(int n) 
{ 
      
// Declare an array to store  
// Fibonacci numbers. 
int []f = new int[n + 2]; 
int i; 
  
// 0th and 1st number of the 
// series are 0 and 1 
f[0] = 0; 
f[1] = 1; 
  
for (i = 2; i <= n; i++)  
{ 
    f[i] = f[i - 1] + f[i - 2]; 
} 
  
return f[n]; 
} 
  
// Function to find N-th term 
// in the series 
static void findNthTerm(int n) 
{ 
// If n is even 
if (n % 2 == 0)  
{ 
    n = n / 2; 
    n = NthPrime(n); 
    Console.WriteLine(n); 
} 
  
// If n is odd 
else 
{ 
    n = (n / 2) + 1; 
    n = NthFib(n - 1); 
    Console.WriteLine(n); 
} 
} 
  
// Driver code 
public static void Main() 
{ 
    int X = 5; 
    findNthTerm(X); 
  
    X = 10; 
    findNthTerm(X); 
} 
} 
  
// This code is contributed  
// by ChitraNayal 

PHP

<?php 
// PHP program to find  
// N-th term in the series 
$MAX = 1000; 
  
// Function to find 
// Nth Prime Number 
function NthPrime($n) 
{ 
    global $MAX; 
    $count = 0; 
    for ($i = 2; $i <= $MAX; $i++) 
    { 
        $check = 0; 
        for ($j = 2;  
             $j <= sqrt($i); $j++)  
        { 
            if ($i % $j == 0) 
            { 
                $check = 1; 
                break; 
            } 
        } 
        if ($check == 0) 
            $count++; 
  
        if ($count == $n)  
        { 
            return $i; 
            break; 
        } 
    } 
} 
  
// Function to find 
// Nth Fibonacci Number 
function NthFib($n) 
{ 
    // Declare an array to store  
    // Fibonacci numbers. 
    $f = array($n + 2); 
  
    // 0th and 1st number of  
    // the series are 0 and 1 
    $f[0] = 0; 
    $f[1] = 1; 
  
    for ($i = 2; $i <= $n; $i++) 
    { 
        $f[$i] = $f[$i - 1] +  
                 $f[$i - 2]; 
    } 
  
    return $f[$n]; 
} 
  
// Function to find N-th  
// term in the series 
function findNthTerm($n) 
{ 
    // If n is even 
    if ($n % 2 == 0) 
    { 
        $n = $n / 2; 
        $n = NthPrime($n); 
        echo $n . "\n"; 
    } 
  
    // If n is odd 
    else 
    { 
        $n = ($n / 2) + 1; 
        $n = NthFib($n - 1); 
        echo $n . "\n"; 
    } 
} 
  
// Driver code 
$X = 5; 
findNthTerm($X); 
  
$X = 10; 
findNthTerm($X); 
  
// This Code is contributed 
// by mits 
?> 

Output:

1
11

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python 3

C#

PHP

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