# 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 write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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