# Sum of numbers from 1 to N which are in Lucas Sequence

Given a number N. The task is to find the sum of numbers from 1 to N, which are present in the Lucas Sequence.

The Lucas numbers are in the following integer sequence:

```2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123 ......
```

Examples:

```Input :  N = 10
Output : 17

Input : N = 5
Output : 10
```

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

Approach:

• Loop through all the Lucas numbers which are less than the given value N.
• Initialize a sum variable with 0.
• Keep on adding these lucas numbers to get the required sum.

Below is the implementation of the above approach:

## C++

 `// C++ program to find sum of numbers from ` `// 1 to N which are in Lucas Sequence ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the ` `// required sum ` `int` `LucasSum(``int` `N) ` `{ ` `    ``// Generate lucas number and keep on ` `    ``// adding them ` `    ``int` `sum = 0; ` `    ``int` `a = 2, b = 1, c; ` ` `  `    ``sum += a; ` ` `  `    ``while` `(b <= N) { ` ` `  `        ``sum += b; ` `        ``int` `c = a + b; ` `        ``a = b; ` `        ``b = c; ` `    ``} ` ` `  `    ``return` `sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `N = 20; ` `    ``cout << LucasSum(N); ` `    ``return` `0; ` `} `

## Java

 `// java program to find sum of numbers from ` `// 1 to N which are in Lucas Sequence ` `class` `GFG ` `{ ` ` `  `// Function to return the ` `// required sum ` `static` `int` `LucasSum(``int` `N) ` `{ ` `    ``// Generate lucas number and keep on ` `    ``// adding them ` `    ``int` `sum = ``0``; ` `    ``int` `a = ``2``, b = ``1``, c; ` ` `  `    ``sum += a; ` ` `  `    ``while` `(b <= N) { ` ` `  `        ``sum += b; ` `        ``c = a + b; ` `        ``a = b; ` `        ``b = c; ` `    ``} ` ` `  `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `N = ``20``; ` `    ``System.out.println(LucasSum(N)); ` `     `  `} ` `// This code is contributed by princiraj1992  ` `} `

## Python3

 `# Python3 program to find Sum of  ` `# numbers from 1 to N which are  ` `# in Lucas Sequence ` ` `  `# Function to return the ` `# required Sum ` `def` `LucasSum(N): ` `     `  `    ``# Generate lucas number and  ` `    ``# keep on adding them ` `    ``Sum` `=` `0` `    ``a ``=` `2` `    ``b ``=` `1` `    ``c ``=` `0` ` `  `    ``Sum` `+``=` `a ` ` `  `    ``while` `(b <``=` `N): ` ` `  `        ``Sum` `+``=` `b ` `        ``c ``=` `a ``+` `b ` `        ``a ``=` `b ` `        ``b ``=` `c ` ` `  `    ``return` `Sum` ` `  `# Driver code ` `N ``=` `20` `print``(LucasSum(N)) ` ` `  `# This code is contributed  ` `# by mohit kumar `

## C#

 `// C# program to find sum of numbers from ` `// 1 to N which are in Lucas Sequence ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the ` `// required sum ` `static` `int` `LucasSum(``int` `N) ` `{ ` `    ``// Generate lucas number and keep on ` `    ``// adding them ` `    ``int` `sum = 0; ` `    ``int` `a = 2, b = 1, c; ` ` `  `    ``sum += a; ` ` `  `    ``while` `(b <= N)  ` `    ``{ ` ` `  `        ``sum += b; ` `        ``c = a + b; ` `        ``a = b; ` `        ``b = c; ` `    ``} ` ` `  `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `N = 20; ` `    ``Console.WriteLine(LucasSum(N)); ` `} ` `} ` ` `  `// This code contributed by Rajput-Ji `

## PHP

 ` `

Output:

```46
```

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