Fibonacci Sequence Generator

Generate Fibonacci sequences and work with Fibonacci numbers, golden ratios, and related mathematical concepts.

Quick Start

Basic Usage

The Fibonacci sequence starts with 0, 1, and each subsequent number is the sum of the two preceding ones.

First 10 Fibonacci numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34

Generate First N Numbers

def fibonacci(n):
    """Generate first n Fibonacci numbers."""
    if n \x3C= 0:
        return []
    elif n == 1:
        return [0]
    seq = [0, 1]
    for i in range(2, n):
        seq.append(seq[-1] + seq[-2])
    return seq

Common Operations

Nth Fibonacci Number (0-indexed)

def nth_fibonacci(n):
    """Get the nth Fibonacci number (0-indexed)."""
    a, b = 0, 1
    for _ in range(n):
        a, b = b, a + b
    return a

Check if Number is Fibonacci

import math

def is_fibonacci(x):
    """Check if x is a Fibonacci number."""
    def is_perfect_square(n):
        s = int(math.sqrt(n))
        return s * s == n
    return is_perfect_square(5 * x * x + 4) or is_perfect_square(5 * x * x - 4)

Golden Ratio Approximation

As n increases, the ratio F(n+1)/F(n) approaches the golden ratio φ ≈ 1.618033988749895

Related Sequences

Lucas Numbers

Similar to Fibonacci but starts with 2, 1

Tribonacci

Each number is sum of previous three

Fibonacci Sum

Sum of first n Fibonacci numbers = F(n+2) - 1