# Non Fibonacci Numbers

• Difficulty Level : Medium
• Last Updated : 11 Jul, 2022

Given a positive integer n, the task is to print the nth 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```
Recommended Practice

Below is the implementation of the above idea.

## C++

 `// C++ program to find n'th Fibonacci number` `#include ``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;``}`

## C

 `// C program to find n'th Fibonacci number` `#include`  `// 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()``{``  ``printf``(``"%d"``,nonFibonacci(5));``  ``return` `0;``}` `// This code is contributed by allwink45.`

## 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

 ` 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

 ``

Output :

`10`

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

Now geeks you must be wondering what if we were supposed to print Non-Fibonacci Series in a range, then the code is as follows:

## C++

 `#include ``using` `namespace` `std;` `int` `main()``{``    ``int` `i = 0, j = 1, k, m, no, b;` `    ``// Range is 10``    ``no = 10;``    ``b = 0;``    ``b = 1;` `    ``// Check if range is less equals to 1``    ``if` `(no <= 1) {``        ``cout << ``"You have enter a wrong range"``;``    ``}` `    ``// check if range is greater than 1``    ``// and less equals to 5``    ``else` `if` `(no <= 5 && no > 1) {``        ``cout << ``"\nThere is not any Non-Fibonacci series "``                ``"that lies between 1 to "``             ``<< no << ``" term of Fibonacci Series."``;``    ``}` `    ``// If range is greater than 5``    ``else` `{` `        ``// Loop to calculate fibonacci series till``        ``// range``        ``for` `(m = 2; m < no; m++) {``            ``k = i + j;``            ``i = j;``            ``j = k;` `            ``// Store fibonacci series into b[]``            ``// array``            ``b[m] = k;``        ``}``        ``i = 5;``        ``cout << ``"\nThe Non-Fibonacci series that lies "``                ``"between 1 to "``             ``<< no << ``" term of Fibonacci Series is: \n"``;` `        ``// Loop to calculate Non-Fibonacci``        ``// series``        ``for` `(``int` `ans = 4; ans < b[no - 1]; ans++) {``            ``if` `(ans != b[i])` `                ``// Print Non-Fibonacci Series``                ``cout << ans << ``"  "``;``            ``else``                ``i++;``        ``}``    ``}``    ``return` `0;``}`

## C

 `#include ``#include ``int` `main()``{``    ``int` `i = 0, j = 1, k, m, no, b;` `    ``// Range is 10``    ``no = 10;``    ``b = 0;``    ``b = 1;` `    ``// Check if range is less equals to 1``    ``if` `(no <= 1) {``        ``printf``(``"You have enter a wrong range"``);``    ``}` `    ``// check if range is greater than 1 and less equals to 5``    ``else` `if` `(no <= 5 && no > 1) {``        ``printf``(``"\nThere is not any Non-Fibonacci series "``               ``"that lies between 1 to %d term of "``               ``"Fibonacci Series."``,``               ``no);``    ``}` `    ``// If range is greater than 5``    ``else` `{` `        ``// Loop to calculate fibonacci series till range``        ``for` `(m = 2; m < no; m++) {``            ``k = i + j;``            ``i = j;``            ``j = k;` `            ``// Store fibonacci series into b[] array``            ``b[m] = k;``        ``}` `        ``i = 5;``        ``printf``(``            ``"\nThe Non-Fibonacci series that lies between "``            ``"1 to %d term of Fibonacci Series is: \n"``,``            ``no);` `        ``// Loop to calculate Non-Fibonacci series``        ``for` `(``int` `ans = 4; ans < b[no - 1]; ans++) {``            ``if` `(ans != b[i])` `                ``// Print Non-Fibonacci Series``                ``printf``(``"%d  "``, ans);``            ``else``                ``i++;``        ``}``    ``}``    ``return` `0;``}`

## Java

 `/*package whatever //do not write package name here */` `import` `java.io.*;` `class` `GFG {``    ``int``[] holes = {``21``, ``3``, ``6``};``    ``int` `i = ``0``, j = ``1``, k, m, no;``    ``int``[] b = ``new` `int``[``10``];` `    ``// Range is 10``    ``no = ``10``;``    ``b[``1``] = ``0``;``    ``b[``2``] = ``1``;` `    ``// Check if range is less equals to 1``    ``if` `(no <= ``1``) {``        ``System.out.print(``"You have enter a wrong range"``);``    ``}` `    ``// check if range is greater than 1``    ``// and less equals to 5``    ``else` `if` `(no <= ``5` `&& no > ``1``) {``        ``System.out.print(``"\n"` `+ ``"There is not any Non-Fibonacci series that lies between 1 to"` `+ no +``        ``" term of Fibonacci Series."``);``    ``}` `    ``// If range is greater than 5``    ``else` `{` `        ``// Loop to calculate fibonacci series till``        ``// range``        ``for` `(m = ``2``; m < no; m++) {``            ``k = i + j;``            ``i = j;``            ``j = k;` `            ``// Store fibonacci series into b[]``            ``// array``            ``b[m] = k;``        ``}``        ``i = ``5``;``        ``System.out.println(``"\n"` `+ ``"The Non-Fibonacci series that lies between 1 to "``             ``+ no + ``" term of Fibonacci Series is: "``+ ``"\n"``);` `        ``// Loop to calculate Non-Fibonacci``        ``// series``        ``for` `(``int` `ans = ``4``; ans < b[no - ``1``]; ans++) {``            ``if` `(ans != b[i])` `                ``// Print Non-Fibonacci Series``                ``System.out.print(ans + ``"  "``);``            ``else``                ``i++;``        ``}``    ``}``}` `// This Solution is contributed by shinjanpatra.`

## Python3

 `i ``=` `0``j ``=` `1``b ``=` `[]``no ``=` `10`  `# Range is 10``b.append(``0``)``b.append(``1``)``if``(no <``=` `1``):  ``# Check if range is less equals to 1``    ``print``(``"You have enter a wrong range..."``)``elif``(no <``=` `5` `and` `no > ``1``):  ``# check if range is greater than 1 and less equals to 5``    ``print``(``"\nThere is not any Non-Fibonacci series that lies between 1 to "``,``          ``no, ``" term of Fibonacci Series."``)``else``:  ``# If range is greater than 5``    ``for` `m ``in` `range``(``2``, no):  ``# Loop to calculate fibonacci series till range``        ``k ``=` `i``+``j``        ``i ``=` `j``        ``j ``=` `k``        ``b.append(k)  ``# Store fibonacci series into list b``    ``i ``=` `5``    ``print``(``"\nThe Non-Fibonacci series that lies between 1 to "``,``          ``no, ``" term of Fibonacci Series is:"``)``    ``for` `ans ``in` `range``(``4``, b[no``-``1``]):  ``# Loop to calculate Non-Fibonacci series``        ``if` `ans !``=` `b[i]:``            ``print``(ans, end``=``"  "``)  ``# Print Non-Fibonacci Series``        ``else``:``            ``i ``=` `i``+``1`

## C#

 `// C# code to implement the approach``using` `System;``class` `GFG {` `  ``public` `static` `void` `Main(``string``[] args)``  ``{``    ``int``[] holes = { 21, 3, 6 };``    ``int` `i = 0, j = 1, k, m, no = 10;``    ``int``[] b = ``new` `int``;` `    ``// Range is 10``    ``b = 0;``    ``b = 1;` `    ``// Check if range is less equals to 1``    ``if` `(no <= 1) {``      ``Console.Write(``"You have enter a wrong range"``);``    ``}` `    ``// check if range is greater than 1``    ``// and less equals to 5``    ``else` `if` `(no <= 5 && no > 1) {``      ``Console.Write(``        ``"\n"``        ``+ ``"There is not any Non-Fibonacci series that lies between 1 to"``        ``+ no + ``" term of Fibonacci Series."``);``    ``}` `    ``// If range is greater than 5``    ``else` `{` `      ``// Loop to calculate fibonacci series till``      ``// range``      ``for` `(m = 2; m < no; m++) {``        ``k = i + j;``        ``i = j;``        ``j = k;` `        ``// Store fibonacci series into b[]``        ``// array``        ``b[m] = k;``      ``}``      ``i = 5;``      ``Console.WriteLine(``        ``"\n"``        ``+ ``"The Non-Fibonacci series that lies between 1 to "``        ``+ no + ``" term of Fibonacci Series is: "``);` `      ``// Loop to calculate Non-Fibonacci``      ``// series``      ``for` `(``int` `ans = 4; ans < b[no - 1]; ans++) {``        ``if` `(ans != b[i])` `          ``// Print Non-Fibonacci Series``          ``Console.Write(ans + ``"  "``);``        ``else``          ``i++;``      ``}``    ``}``  ``}``}` `// This Solution is contributed by phasing17`

## Javascript

 ``

Output

```The Non-Fibonacci series that lies between 1 to 10 term of Fibonacci Series is:
4  6  7  9  10  11  12  14  15  16  17  18  19  20  22  23  24  25  26  27  28  29  30  31  32  33  ```

Time Complexity : O(n) , Auxiliary Space : O(n)

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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