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

Last Updated : 28 May, 2022

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```

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] = 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

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## Javascript

 ``

Output:

```1
11```

Time Complexity: O(MAX*sqrt(MAX)), where MAX represents a defined constant.
Auxiliary Space: O(X), where X represents the given integer.