# 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 = 10Output :17Input :N = 5Output :10

**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 <bits/stdc++.h> ` `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; ` `} ` |

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## 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 ` `} ` |

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## 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 ` |

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## 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 ` |

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## PHP

`<?php ` `// PHP program to find sum of numbers from ` `// 1 to N which are in Lucas Sequence ` ` ` `// Function to return the required sum ` `function` `LucasSum(` `$N` `) ` `{ ` ` ` `// Generate lucas number and ` ` ` `// keep on adding them ` ` ` `$sum` `= 0; ` ` ` `$a` `= 2; ` `$b` `= 1; ` `$c` `; ` ` ` ` ` `$sum` `+= ` `$a` `; ` ` ` ` ` `while` `(` `$b` `<= ` `$N` `) ` ` ` `{ ` ` ` `$sum` `+= ` `$b` `; ` ` ` `$c` `= ` `$a` `+ ` `$b` `; ` ` ` `$a` `= ` `$b` `; ` ` ` `$b` `= ` `$c` `; ` ` ` `} ` ` ` ` ` `return` `$sum` `; ` `} ` ` ` `// Driver code ` `$N` `= 20; ` `echo` `(LucasSum(` `$N` `)); ` ` ` `// This code is contributed ` `// by Code_Mech. ` `?> ` |

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**Output:**

46

## Recommended Posts:

- Longest sub-sequence of array containing Lucas numbers
- Lucas Numbers
- Jacobsthal and Jacobsthal-Lucas numbers
- Find a sequence of N prime numbers whose sum is a composite number
- Lucas Primality Test
- Compute nCr % p | Set 2 (Lucas Theorem)
- Primality Test | Set 5(Using Lucas-Lehmer Series)
- Sum of the sequence 2, 22, 222, .........
- Look-and-Say Sequence
- Sylvester's sequence
- Golomb sequence
- Increasing sequence with given GCD
- Alcuin's Sequence
- Recaman's sequence
- Gould's Sequence

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