# 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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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 ` `?> ` |

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**Output:**

38

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