Lucas Series Calculator

What is Lucas Series?

The Lucas series is a sequence of integers similar to the Fibonacci sequence. It starts with 2 and 1 as its first two terms, and each subsequent number is the sum of the two preceding ones. This sequence has interesting mathematical properties and appears in various applications in number theory and computer science.

How to Calculate Lucas Series

To calculate Lucas numbers, start with L₀ = 2 and L₁ = 1, then generate each subsequent number by adding the two previous numbers in the sequence. This process continues indefinitely, creating the Lucas series.

Formula

The formula for calculating the nth Lucas number is:

\[ L_n = L_{n-1} + L_{n-2} \]

Where L_n is the nth Lucas number, with initial conditions L₀ = 2 and L₁ = 1.

Calculation Steps

1. Start with L₀ = 2 and L₁ = 1
2. For each subsequent number n, calculate L_n = L_n-1 + L_n-2
3. Continue this process for as many numbers as needed in the sequence

Example

Let's calculate the first 8 Lucas numbers:

1. L₀ = 2
2. L₁ = 1
3. L₂ = L₁ + L₀ = 1 + 2 = 3
4. L₃ = L₂ + L₁ = 3 + 1 = 4
5. L₄ = L₃ + L₂ = 4 + 3 = 7
6. L₅ = L₄ + L₃ = 7 + 4 = 11
7. L₆ = L₅ + L₄ = 11 + 7 = 18
8. L₇ = L₆ + L₅ = 18 + 11 = 29

Therefore, the first 8 Lucas numbers are: 2, 1, 3, 4, 7, 11, 18, 29