# 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:

1. Terms at odd positions in the given series forms fibonacci series.
2. 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.

Below is the implementation of above approach:

## C++

 `// CPP program to find N-th term ` `// in the series ` `#include ` `#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; ` `    ``f = 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; ` `f = 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

 ` `

Output:

```1
11
```

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