# Non Fibonacci Numbers

Given a positive integer n, the task is to print the n’th non Fibonacci number. The Fibonacci numbers are defined as:

Fib(0) = 0 Fib(1) = 1 for n >1, Fib(n) = Fib(n-1) + Fib(n-2)

First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 141, ……..**Examples :**

Input : n = 2 Output : 6 Input : n = 5 Output : 10

A** naive solution** is to find find Fibonacci numbers and then print first n numbers not present in the found Fibonacci numbers.

A **better solution **is to use the formula of Fibonacci numbers and keep adding of gap between two consecutive Fibonacci numbers. Value of sum of gap is count of non-fibonacci numbers seen so far. Below is implementation of above idea.

## C++

`// C++ program to find n'th Fibonacci number` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Returns n'th Non-Fibonacci number` `int` `nonFibonacci(` `int` `n)` `{` ` ` `// curr is to keep track of current fibonacci` ` ` `// number, prev is previous, prevPrev is` ` ` `// previous of previous.` ` ` `int` `prevPrev=1, prev=2, curr=3;` ` ` `// While count of non-fibonacci numbers` ` ` `// doesn't become negative or zero` ` ` `while` `(n > 0)` ` ` `{` ` ` `// Simple Fibonacci number logic` ` ` `prevPrev = prev;` ` ` `prev = curr;` ` ` `curr = prevPrev + prev;` ` ` `// (curr - prev - 1) is count of` ` ` `// non-Fibonacci numbers between curr` ` ` `// and prev.` ` ` `n = n - (curr - prev - 1);` ` ` `}` ` ` `// n might be negative now. Make sure it` ` ` `// becomes positive by removing last added` ` ` `// gap.` ` ` `n = n + (curr - prev - 1);` ` ` `// n must be now positive and less than or equal` ` ` `// to gap between current and previous, i.e.,` ` ` `// (curr - prev - 1);` ` ` `// Now add the positive n to previous Fibonacci` ` ` `// number to find the n'th non-fibonacci.` ` ` `return` `prev + n;` `}` `// Driver code` `int` `main()` `{` ` ` `cout << nonFibonacci(5);` ` ` `return` `0;` `}` |

## Java

`// Java program to find` `// n'th Fibonacci number` `import` `java.io.*;` `class` `GFG` `{` ` ` `// Returns n'th Non-` ` ` `// Fibonacci number` ` ` `static` `int` `nonFibonacci(` `int` `n)` ` ` `{` ` ` ` ` `// curr is to keep track of` ` ` `// current fibonacci number,` ` ` `// prev is previous, prevPrev` ` ` `// is previous of previous.` ` ` `int` `prevPrev = ` `1` `, prev = ` `2` `, curr = ` `3` `;` ` ` `// While count of non-fibonacci` ` ` `// numbers doesn't become` ` ` `// negative or zero` ` ` `while` `(n > ` `0` `)` ` ` `{` ` ` `// Simple Fibonacci number logic` ` ` `prevPrev = prev;` ` ` `prev = curr;` ` ` `curr = prevPrev + prev;` ` ` `// (curr - prev - 1) is count` ` ` `// of non-Fibonacci numbers` ` ` `// between curr and prev.` ` ` `n = n - (curr - prev - ` `1` `);` ` ` `}` ` ` `// n might be negative now. Make` ` ` `// sure it becomes positive by` ` ` `// removing last added gap.` ` ` `n = n + (curr - prev - ` `1` `);` ` ` `// n must be now positive and less` ` ` `// than or equal to gap between` ` ` `// current and previous, i.e.,` ` ` `// (curr - prev - 1);` ` ` `// Now add the positive n to` ` ` `// previous Fibonacci number` ` ` `// to find the n'th non-fibonacci.` ` ` `return` `prev + n;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main (String args[])` ` ` `{` ` ` `System.out.println(nonFibonacci(` `5` `));` ` ` `}` `}` `// This code is contributed by aj_36` |

## Python

`# Python program to find n'th` `# Fibonacci number` `# Returns n'th Non-Fibonacci` `# number` `def` `nonFibonacci(n):` ` ` `# curr is to keep track of` ` ` `# current fibonacci number,` ` ` `# prev is previous, prevPrev` ` ` `# is previous of previous.` ` ` `prevPrev ` `=` `1` ` ` `prev ` `=` `2` ` ` `curr ` `=` `3` ` ` `# While count of non-fibonacci` ` ` `# numbers doesn't become` ` ` `# negative or zero` ` ` `while` `n > ` `0` `:` ` ` `prevPrev ` `=` `prev` ` ` `prev ` `=` `curr` ` ` `curr ` `=` `prevPrev ` `+` `prev` ` ` ` ` `# (curr - prev - 1) is` ` ` `# count of non-Fibonacci` ` ` `# numbers between curr` ` ` `# and prev.` ` ` `n ` `=` `n ` `-` `(curr ` `-` `prev ` `-` `1` `)` ` ` ` ` `# n might be negative now.` ` ` `# Make sure it becomes positive` ` ` `# by removing last added gap.` ` ` `n ` `=` `n ` `+` `(curr ` `-` `prev ` `-` `1` `)` ` ` ` ` `# n must be now positive and` ` ` `# less than or equal to gap` ` ` `# between current and previous,` ` ` `# i.e., (curr - prev - 1)` ` ` ` ` `# Now add the positive n to` ` ` `# previous Fibonacci number to` ` ` `# find the n'th non-fibonacci.` ` ` `return` `prev ` `+` `n` `# Driver code` `print` `(nonFibonacci(` `5` `))` `# This code is contributed by anuj_67.` |

## C#

`// C# program to find` `// n'th Fibonacci number` `using` `System;` `class` `GFG` `{` ` ` `// Returns n'th Non-` ` ` `// Fibonacci number` ` ` `static` `int` `nonFibonacci (` `int` `n)` ` ` `{` ` ` ` ` `// curr is to keep track of` ` ` `// current fibonacci number,` ` ` `// prev is previous, prevPrev` ` ` `// is previous of previous.` ` ` `int` `prevPrev = 1, prev = 2, curr = 3;` ` ` `// While count of non-fibonacci` ` ` `// numbers doesn't become` ` ` `// negative or zero` ` ` `while` `(n > 0)` ` ` `{` ` ` `// Simple Fibonacci number logic` ` ` `prevPrev = prev;` ` ` `prev = curr;` ` ` `curr = prevPrev + prev;` ` ` `// (curr - prev - 1) is count` ` ` `// of non-Fibonacci numbers` ` ` `// between curr and prev.` ` ` `n = n - (curr - prev - 1);` ` ` `}` ` ` `// n might be negative now. Make` ` ` `// sure it becomes positive by` ` ` `// removing last added gap.` ` ` `n = n + (curr - prev - 1);` ` ` `// n must be now positive and less` ` ` `// than or equal to gap between ` ` ` `// current and previous, i.e.,` ` ` `// (curr - prev - 1);` ` ` `// Now add the positive n to` ` ` `// previous Fibonacci number` ` ` `// to find the n'th non-fibonacci.` ` ` `return` `prev + n;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main ()` ` ` `{` ` ` `Console.WriteLine (nonFibonacci(5));` ` ` `}` `}` `//This code is contributed by aj_36` |

## PHP

`<?php` `// PHP program to find` `// n'th Fibonacci number` `// Returns n'th Non-` `// Fibonacci number` `function` `nonFibonacci(` `$n` `)` `{` ` ` `// curr is to keep track of` ` ` `// current fibonacci number,` ` ` `// prev is previous, prevPrev` ` ` `// is previous of previous.` ` ` `$prevPrev` `= 1;` ` ` `$prev` `= 2;` ` ` `$curr` `= 3;` ` ` `// While count of non-fibonacci` ` ` `// numbers doesn't become` ` ` `// negative or zero` ` ` `while` `(` `$n` `> 0)` ` ` `{` ` ` `// Simple Fibonacci` ` ` `// number logic` ` ` `$prevPrev` `= ` `$prev` `;` ` ` `$prev` `= ` `$curr` `;` ` ` `$curr` `= ` `$prevPrev` `+ ` `$prev` `;` ` ` `// (curr - prev - 1) is count` ` ` `// of non-Fibonacci numbers` ` ` `// between curr and prev.` ` ` `$n` `= ` `$n` `- (` `$curr` `- ` `$prev` `- 1);` ` ` `}` ` ` `// n might be negative now. Make` ` ` `// sure it becomes positive by` ` ` `// removing last added gap.` ` ` `$n` `= ` `$n` `+ (` `$curr` `- ` `$prev` `- 1);` ` ` `// n must be now positive and` ` ` `// less than or equal to gap` ` ` `// between current and previous, ` ` ` `// i.e., (curr - prev - 1);` ` ` `// Now add the positive n to` ` ` `// previous Fibonacci number` ` ` `// to find the n'th non-fibonacci.` ` ` `return` `$prev` `+ ` `$n` `;` `}` `// Driver code` `echo` `nonFibonacci(5);` `// This code is contributed by m_kit` `?>` |

## Javascript

`<script>` `// Javascript program to find n'th Fibonacci number` `// Returns n'th Non-Fibonacci number` `function` `nonFibonacci(n)` `{` ` ` `// curr is to keep track of current fibonacci` ` ` `// number, prev is previous, prevPrev is` ` ` `// previous of previous.` ` ` `let prevPrev=1, prev=2, curr=3;` ` ` `// While count of non-fibonacci numbers` ` ` `// doesn't become negative or zero` ` ` `while` `(n > 0)` ` ` `{` ` ` `// Simple Fibonacci number logic` ` ` `prevPrev = prev;` ` ` `prev = curr;` ` ` `curr = prevPrev + prev;` ` ` `// (curr - prev - 1) is count of` ` ` `// non-Fibonacci numbers between curr` ` ` `// and prev.` ` ` `n = n - (curr - prev - 1);` ` ` `}` ` ` `// n might be negative now. Make sure it` ` ` `// becomes positive by removing last added` ` ` `// gap.` ` ` `n = n + (curr - prev - 1);` ` ` `// n must be now positive and less than or equal` ` ` `// to gap between current and previous, i.e.,` ` ` `// (curr - prev - 1);` ` ` `// Now add the positive n to previous Fibonacci` ` ` `// number to find the n'th non-fibonacci.` ` ` `return` `prev + n;` `}` `// Driver code` ` ` `document.write(nonFibonacci(5));` `// This code is contributed by Mayank Tyagi` `</script>` |

**Output :**

10

**Time Complexity : **O(n) **Auxiliary Space : **O(1)

The above problem and solution are contributed by **Hemang Sarkar**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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