# Find M-th number whose repeated sum of digits of a number is N

Given two positive integers N and M. The task is to find M-th number whose sum of digits of a number until sum becomes single digit is N.

**Examples:**

Input:N = 1, M = 3Output:19 The first two numbers being 1 and 9.Input:N = 2, M = 5Output:38 The first four numbers being 2, 11, 20 and 29.

A **naive** approach is to iterate for all numbers and keep a count of number whose sum returns N.

An **efficient** approach is to find the summation of digits till it becomes single digits in O(1) that has been discussed here. Hence the formula to find M-th number will be:

M

^{th}number: (M-1)*9 + N

Below is the implementation of the above approach:

## C++

`// C++ program to Find m-th number whose ` `// sum of digits of a number until ` `// sum becomes single digit is N ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the M-th ` `// number whosesum till one digit is N ` `int` `findNumber(` `int` `n, ` `int` `m) ` `{ ` ` ` `int` `num = (m - 1) * 9 + n; ` ` ` `return` `num; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` ` ` `int` `n = 2, m = 5; ` ` ` `cout << findNumber(n, m); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

// Java program to Find m-th number whose

// sum of digits of a number until

// sum becomes single digit is N

class GFG

{

// Function to find the M-th

// number whosesum till one digit is N

static int findNumber(int n, int m)

{

int num = (m – 1) * 9 + n;

return num;

}

// Driver Code

public static void main(String args[])

{

int n = 2, m = 5;

System.out.print(findNumber(n, m));

}

}

// This code is contributed

// by Akanksha Rai

## Python3

`# Python3 program to Find m-th number ` `# whose sum of digits of a number ` `# until sum becomes single digit is N ` ` ` `# Function to find the M-th ` `# number whosesum till one digit is N ` `def` `findNumber(n, m) : ` ` ` ` ` `num ` `=` `(m ` `-` `1` `) ` `*` `9` `+` `n; ` ` ` `return` `num; ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `n ` `=` `2` `; ` ` ` `m ` `=` `5` `; ` ` ` `print` `(findNumber(n, m)) ` ` ` `# This code is contributed by Ryuga ` |

*chevron_right*

*filter_none*

## C#

`// C# program to Find m-th number whose ` `// sum of digits of a number until ` `// sum becomes single digit is N ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the M-th ` `// number whosesum till one digit is N ` `static` `int` `findNumber(` `int` `n, ` `int` `m) ` `{ ` ` ` `int` `num = (m - 1) * 9 + n; ` ` ` `return` `num; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `n = 2, m = 5; ` ` ` `Console.Write(findNumber(n, m)); ` `} ` `} ` ` ` `// This code is contributed ` `// by Akanksha Rai ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// PHP program to Find m-th number whose ` `// sum of digits of a number until ` `// sum becomes single digit is N ` ` ` `// number whosesum till one digit is N ` `function` `findNumber(` `$n` `, ` `$m` `) ` `{ ` ` ` `$num` `= (` `$m` `- 1) * 9 + ` `$n` `; ` ` ` `return` `$num` `; ` `} ` ` ` `// Driver Code ` `$n` `= 2; ` `$m` `= 5; ` `echo` `findNumber(` `$n` `, ` `$m` `); ` ` ` `// This code is contributed ` `// by Akanksha Rai ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

38

## Recommended Posts:

- Remove repeated digits in a given number
- Recursive sum of digits of a number formed by repeated appends
- Count ways to spell a number with repeated digits
- Find the Largest number with given number of digits and sum of digits
- Find smallest number with given number of digits and sum of digits
- Find maximum number that can be formed using digits of a given number
- Find count of digits in a number that divide the number
- Find the smallest number whose digits multiply to a given number n
- Given a number n, find the first k digits of n^n
- Find first and last digits of a number
- Find a number x such that sum of x and its digits is equal to given n.
- Find the n-th number made of even digits only
- Find sum of digits in factorial of a number
- Find next greater number with same set of digits
- Find the total Number of Digits in (N!)N

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.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.