# N-th term in the series 1, 11, 55, 239, 991,….

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

1, 11, 55, 239, 991, …

Examples:

```Input: N = 3
Output: 55

Input: N = 4
Output: 239
```

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

Approach-1: On writing down the binary representation of the given numbers, a pattern can be observed.

1 = 1
11 = 1011
55 = 110111
239 = 11101111
.
.
.

Hence for N = 1, the answer will always be one. For N-th term the binary string will be (n-1)*1 + (0) + (n)*1 which is converted to decimal value to get the answer.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the N-th term ` `// in 1, 11, 55, 239, 991, .... ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the decimal value ` `// of a binary number ` `int` `binaryToDecimal(string n) ` `{ ` `    ``string num = n; ` `    ``int` `dec_value = 0; ` ` `  `    ``// Initializing base value to 1, i.e 2^0 ` `    ``int` `base = 1; ` ` `  `    ``int` `len = num.length(); ` `    ``for` `(``int` `i = len - 1; i >= 0; i--) { ` `        ``if` `(num[i] == ``'1'``) ` `            ``dec_value += base; ` `        ``base = base * 2; ` `    ``} ` ` `  `    ``return` `dec_value; ` `} ` ` `  `// find the binary representation ` `// of the N-th number in sequence ` `int` `numberSequence(``int` `n) ` `{ ` `    ``// base case ` `    ``if` `(n == 1) ` `        ``return` `1; ` ` `  `    ``// answer string ` `    ``string s = ``""``; ` ` `  `    ``// add n-1 1's ` `    ``for` `(``int` `i = 1; i < n; i++) ` `        ``s += ``'1'``; ` ` `  `    ``// add 0 ` `    ``s += ``'0'``; ` ` `  `    ``// add n 1's at end ` `    ``for` `(``int` `i = 1; i <= n; i++) ` `        ``s += ``'1'``; ` ` `  `    ``int` `num = binaryToDecimal(s); ` ` `  `    ``return` `num; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `n = 4; ` ` `  `    ``cout << numberSequence(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find the N-th  ` `// term in 1, 11, 55, 239, 991, .... ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the decimal ` `// value of a binary number ` `static` `int` `binaryToDecimal(String n) ` `{ ` `    ``String num = n; ` `    ``int` `dec_value = ``0``; ` ` `  `    ``// Initializing base ` `    ``// value to 1, i.e 2^0 ` `    ``int` `base = ``1``; ` ` `  `    ``int` `len = num.length(); ` `    ``for` `(``int` `i = len - ``1``; i >= ``0``; i--) ` `    ``{ ` `        ``if` `(num.charAt(i) == ``'1'``) ` `            ``dec_value += base; ` `        ``base = base * ``2``; ` `    ``} ` ` `  `    ``return` `dec_value; ` `} ` ` `  `// find the binary representation ` `// of the N-th number in sequence ` `static` `int` `numberSequence(``int` `n) ` `{ ` `    ``// base case ` `    ``if` `(n == ``1``) ` `        ``return` `1``; ` ` `  `    ``// answer string ` `    ``String s = ``""``; ` ` `  `    ``// add n-1 1's ` `    ``for` `(``int` `i = ``1``; i < n; i++) ` `        ``s += ``'1'``; ` ` `  `    ``// add 0 ` `    ``s += ``'0'``; ` ` `  `    ``// add n 1's at end ` `    ``for` `(``int` `i = ``1``; i <= n; i++) ` `        ``s += ``'1'``; ` ` `  `    ``int` `num = binaryToDecimal(s); ` ` `  `    ``return` `num; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `n = ``4``; ` ` `  `    ``System.out.println(numberSequence(n)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by Arnab Kundu `

## Python 3

 `# Python 3 program to find the N-th term ` `# in 1, 11, 55, 239, 991, .... ` `  `  `# Function to return the decimal value ` `# of a binary number ` `def` `binaryToDecimal(n): ` ` `  `    ``num ``=` `n ` `    ``dec_value ``=` `0` `  `  `    ``# Initializing base value to 1, i.e 2^0 ` `    ``base ``=` `1` `  `  `    ``l ``=` `len``(num) ` `    ``for` `i ``in` `range``(l ``-` `1``,``-``1``, ``-``1``): ` `        ``if` `(num[i] ``=``=` `'1'``): ` `            ``dec_value ``+``=` `base ` `        ``base ``=` `base ``*` `2` `  `  `    ``return` `dec_value ` `  `  `# find the binary representation ` `# of the N-th number in sequence ` `def` `numberSequence(n): ` `     `  `    ``# base case ` `    ``if` `(n ``=``=` `1``): ` `        ``return` `1` `  `  `    ``# answer string ` `    ``s ``=` `"" ` `  `  `    ``# add n-1 1's ` `    ``for` `i ``in` `range``(``1``, n): ` `        ``s ``+``=` `'1'` `  `  `    ``# add 0 ` `    ``s ``+``=` `'0'` `  `  `    ``# add n 1's at end ` `    ``for` `i ``in` `range``(``1``,n``+``1``): ` `        ``s ``+``=` `'1'` `  `  `    ``num ``=` `binaryToDecimal(s) ` `  `  `    ``return` `num ` `  `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `     `  `    ``n ``=` `4` `  `  `    ``print``(numberSequence(n)) ` ` `  `# this code is contributed by ChitraNayal `

## C#

 `// C# program to find the N-th  ` `// term in 1, 11, 55, 239, 991, .... ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the decimal ` `// value of a binary number ` `static` `int` `binaryToDecimal(String n) ` `{ ` `    ``String num = n; ` `    ``int` `dec_value = 0; ` ` `  `    ``// Initializing base ` `    ``// value to 1, i.e 2^0 ` `    ``int` `base_ = 1; ` ` `  `    ``int` `len = num.Length; ` `    ``for` `(``int` `i = len - 1; i >= 0; i--) ` `    ``{ ` `        ``if` `(num[i] == ``'1'``) ` `            ``dec_value += base_; ` `        ``base_ = base_ * 2; ` `    ``} ` ` `  `    ``return` `dec_value; ` `} ` ` `  `// find the binary representation ` `// of the N-th number in sequence ` `static` `int` `numberSequence(``int` `n) ` `{ ` `    ``// base case ` `    ``if` `(n == 1) ` `        ``return` `1; ` ` `  `    ``// answer string ` `    ``String s = ``""``; ` ` `  `    ``// add n-1 1's ` `    ``for` `(``int` `i = 1; i < n; i++) ` `        ``s += ``'1'``; ` ` `  `    ``// add 0 ` `    ``s += ``'0'``; ` ` `  `    ``// add n 1's at end ` `    ``for` `(``int` `i = 1; i <= n; i++) ` `        ``s += ``'1'``; ` ` `  `    ``int` `num = binaryToDecimal(s); ` ` `  `    ``return` `num; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `n = 4; ` ` `  `    ``Console.WriteLine(numberSequence(n)); ` `} ` `} ` ` `  `// This code is contributed ` `// by Subhadeep `

## PHP

 `= 0; ``\$i``--)  ` `    ``{ ` `        ``if` `(``\$num``[``\$i``] == ``'1'``) ` `            ``\$dec_value` `+= ``\$base``; ` `        ``\$base` `= ``\$base` `* 2; ` `    ``} ` ` `  `    ``return` `\$dec_value``; ` `} ` ` `  `// find the binary representation ` `// of the N-th number in sequence ` `function` `numberSequence(``\$n``) ` `{ ` `    ``// base case ` `    ``if` `(``\$n` `== 1) ` `        ``return` `1; ` ` `  `    ``// answer string ` `    ``\$s` `= ``""``; ` ` `  `    ``// add n-1 1's ` `    ``for` `(``\$i` `= 1; ``\$i` `< ``\$n``; ``\$i``++) ` `        ``\$s` `.= ``'1'``; ` ` `  `    ``// add 0 ` `    ``\$s` `.= ``'0'``; ` ` `  `    ``// add n 1's at end ` `    ``for` `(``\$i` `= 1; ``\$i` `<= ``\$n``; ``\$i``++) ` `        ``\$s` `.= ``'1'``; ` ` `  `    ``\$num` `= binaryToDecimal(``\$s``); ` ` `  `    ``return` `\$num``; ` `} ` ` `  `// Driver Code ` `\$n` `= 4; ` ` `  `echo` `numberSequence(``\$n``); ` ` `  `// This code is contributed by mits ` `?> `

Output:

```239
```

Approach-2: The series has a general formulae of 4N-2N-1 which is used to get the N-th term in series.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the N-th term ` `// in 1, 11, 55, 239, 991, .... ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the N-th term ` `int` `numberSequence(``int` `n) ` `{ ` `    ``// calculates the N-th term ` `    ``int` `num = ``pow``(4, n) - ``pow``(2, n) - 1; ` ` `  `    ``return` `num; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `n = 4; ` ` `  `    ``cout << numberSequence(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find the N-th  ` `// term in 1, 11, 55, 239, 991, .... ` `class` `GFG ` `{ ` `// Function to find the N-th term ` `static` `int` `numberSequence(``int` `n) ` `{ ` `    ``// calculates the N-th term ` `    ``int` `num = (``int``)(Math.pow(``4``, n) -  ` `                    ``Math.pow(``2``, n)) - ``1``; ` ` `  `    ``return` `num; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``int` `n = ``4``; ` ` `  `    ``System.out.println(numberSequence(n)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by Arnab Kundu `

## Python 3

 `# Python 3 program to find N-th term  ` `# in 1, 11, 55, 239, 991, ....  ` ` `  `# calculate Nth term of series ` `def` `numberSequence(n) : ` ` `  `    ``# calculates the N-th term  ` `    ``num ``=` `pow``(``4``, n) ``-` `pow``(``2``, n) ``-` `1` ` `  `    ``return` `num ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"` `: ` ` `  `    ``n ``=` `4` `     `  `    ``print``(numberSequence(n)) ` ` `  `# This code is contributed by ANKITRAI1 `

## C#

 `// C# program to find the N-th  ` `// term in 1, 11, 55, 239, 991, .... ` `using` `System; ` ` `  `class` `GFG ` `{ ` `// Function to find the N-th term ` `static` `int` `numberSequence(``int` `n) ` `{ ` `    ``// calculates the N-th term ` `    ``int` `num = (``int``)(Math.Pow(4, n) -  ` `                    ``Math.Pow(2, n)) - 1; ` ` `  `    ``return` `num; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `n = 4; ` ` `  `    ``Console.WriteLine(numberSequence(n)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by chandan_jnu. `

## PHP

 ` `

Output:

```239
```

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