Fibonacci Number Generator

Fibonacci Number Generator

Generate Fibonacci sequences up to 1,000 terms or up to a maximum value, check whether a number is in the Fibonacci sequence, explore golden ratio convergence, and compare related sequences like Lucas, Tribonacci, and Pell numbers. Supports BigInt for arbitrarily large values with instant computation.

How to Use

Choose a generation mode: “First N terms” to specify how many Fibonacci numbers to generate (up to 1,000), or “Up to value” to generate all Fibonacci numbers below a given limit. Optionally change the starting values from the default 0 and 1 to create generalized Fibonacci sequences. Use the checker to test whether any number is a Fibonacci number and find its index. Explore the golden ratio table to see how consecutive ratios converge to φ.

Features

• Sequence Generator — Generate up to 1,000 Fibonacci terms or all terms up to a maximum value. Formatted output with term indices, stats showing term count, largest value, and digit count.
• Custom Starting Values — Change from the standard 0, 1 to any starting pair for generalized Fibonacci sequences. Explore how different seeds produce different sequences with the same additive structure.
• Fibonacci Checker — Enter any number to check if it’s a Fibonacci number. Shows the term index if found, nearest Fibonacci numbers above and below, and distance to the closest Fibonacci number.
• Golden Ratio Convergence — Table showing F(n)/F(n-1) ratios approaching φ (1.6180339887…). See the difference from φ shrink with each term, with visual convergence indicator.
• Special Sequences — Toggle between Lucas Numbers (2, 1, 3, 4, 7…), Tribonacci Numbers (0, 0, 1, 1, 2, 4, 7, 13…), and Pell Numbers (0, 1, 2, 5, 12, 29…) with the same formatting.
• Export — Copy the full sequence or download as .txt file.
• Reference — History of the Fibonacci sequence, connections to nature (spirals, phyllotaxis), golden ratio, and applications in computer science.

About the Fibonacci Sequence

The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… Named after Leonardo of Pisa (Fibonacci), who introduced it to Western mathematics in his 1202 book Liber Abaci through the famous rabbit population problem, the sequence was known to Indian mathematicians centuries earlier. Fibonacci numbers appear throughout nature in spiral arrangements of seeds, petals, and shells, and have important applications in algorithms, data structures, and financial analysis.