# Calculator that checks if a number is in the Fibonacci sequence

Use the calculator below to check if almost any number is a Fibonacci one.

### Is a Fibonacci Number? Calculator

Please fill in a number to check if it is a Fibonacci number:

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## What is a Fibonacci number?

A Fibonacci number should obey this sequence of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The first Fibonacci number (F_{0}) is zero and the second (F_{1}) and the third (F_{1}) are one.

To get the next Fibonacci number, we just need to addup the two numbers before it. For Example:

- The 4th (F
_{3}) is found by adding the two numbers before it (1+1) - The 5th (F
_{2}) is also found by adding the two numbers before it (1+2); - The 6th (F
_{4}) is 2+3 = 5 - ...
- The 10th (F
_{9}) is (13+21) = 34

and so on ...

You get the idea!

So, we can derive the following formula to calculate any fibonacci number:

_{0}= 0, F

_{1}= 1

and

_{n}= F

_{n - 2}+ F

_{n - 1}

for n > 1.

## Fibonacci Chart

n | F_{n} |
---|---|

0 | 0 |

1 | 1 |

2 | 1 |

3 | 2 |

4 | 3 |

5 | 5 |

6 | 8 |

7 | 13 |

8 | 21 |

9 | 34 |

10 | 55 |

11 | 89 |

12 | 144 |

13 | 233 |

14 | 377 |

15 | 610 |

The fibonacii sequence grows very fast. For example:

F_{0} = 0,

F_{10} = 34,

F_{20} = 4181,

F_{30} = 514229,

F_{40} = 63245986,

F_{50} = 7778742049,

F_{100} = 218922995834555169026,

F_{200} = 173402521172797813159685037284371942044301,

F_{500} = 86168291600238450732788312165664788095941068326060883324529903470149056115823592713458328176574447204501,

F_{1000} = 26863810024485359386146727202142923967616609318986952340123175997617981700247881689338369654483356564191827856161443356312976673642210350324634850410377680367334151172899169723197082763985615764450078474174626,

You get the idea!

That is why the best way to work with Fibonacci numbers is by using a calculator or a table.

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