Sum of digits written in different bases from 2 to n-1

08 Apr, 2021
Given a number n, find the sum of digits of n when represented in different bases from 2 to n-1.Examples:  
Input : 5
Output : 2 3 2
Representation of 5 is 101, 12, 11 in bases 2 , 3 , 4 .

Input : 7
Output : 3 3 4 3 2
 
 
As the given question wants the sum of digits in different bases, first we have to calculate the given number of different bases and add each digit to the number of different bases.So, to calculate each number’s representation we will take the mod of given number by the base in which we want to represent that number.Then, we have to add all those mod values as the mod values obtained will represent that number in that base.Finally, the sum of those mod values gives the sum of digits of that number.
As the given question wants the sum of digits in different bases, first we have to calculate the given number of different bases and add each digit to the number of different bases.
So, to calculate each number’s representation we will take the mod of given number by the base in which we want to represent that number.
Then, we have to add all those mod values as the mod values obtained will represent that number in that base.
Finally, the sum of those mod values gives the sum of digits of that number.
Below are implementations of this approach 
 
C++
Java
Python3
C#
PHP
Javascript
// CPP program to find sum of digits of// n in different bases from 2 to n-1.#include <bits/stdc++.h>using namespace std; // function to calculate sum of// digit for a given baseint solve(int n, int base){    // Sum of digits    int result = 0 ;         // Calculating the number (n) by    // taking mod with the base and adding    // remainder to the result and    // parallelly reducing the num value .    while (n > 0)    {        int remainder = n % base ;        result = result + remainder ;        n = n / base;    }         // returning the result    return result ;} void printSumsOfDigits(int n){    // function calling for multiple bases    for (int base = 2 ; base < n ; ++base)           cout << solve(n, base) <<" ";} // Driver programint main(){    int n = 8;    printSumsOfDigits(n);    return 0;}
// Java program to find sum of digits of// n in different bases from 2 to n-1.class GFG{// function to calculate sum of// digit for a given basestatic int solve(int n, int base){    // Sum of digits    int result = 0 ;         // Calculating the number (n) by    // taking mod with the base and adding    // remainder to the result and    // parallelly reducing the num value .    while (n > 0)    {        int remainder = n % base ;        result = result + remainder ;        n = n / base;    }         // returning the result    return result ;} static void printSumsOfDigits(int n){    // function calling for multiple bases    for (int base = 2 ; base < n ; ++base)        System.out.print(solve(n, base)+" ");} // Driver Codepublic static void main(String[] args){    int n = 8;    printSumsOfDigits(n);}}// This code is contributed by Smitha
# Python program to find sum of digits of# n in different bases from 2 to n-1.  # def to calculate sum of# digit for a given basedef solve(n, base) :          # Sum of digits    result = 0          # Calculating the number (n) by    # taking mod with the base and adding    # remainder to the result and    # parallelly reducing the num value .    while (n > 0) :             remainder = n % base        result = result + remainder         n = int(n / base)          # returning the result    return result  def printSumsOfDigits(n) :          # def calling for    # multiple bases    for base in range(2, n) :        print (solve(n, base), end=" ") # Driver coden = 8printSumsOfDigits(n)  # This code is contributed by Manish Shaw# (manishshaw1)
// Java program to find the sum of digits of// n in different base1s from 2 to n-1.using System; class GFG{// function to calculate sum of// digit for a given base1static int solve(int n, int base1){    // Sum of digits    int result = 0 ;         // Calculating the number (n) by    // taking mod with the base1 and adding    // remainder to the result and    // parallelly reducing the num value .    while (n > 0)    {        int remainder = n % base1 ;        result = result + remainder ;        n = n / base1;    }         // returning the result    return result ;} static void printSumsOfDigits(int n){    // function calling for multiple base1s    for (int base1 = 2 ; base1 < n ; ++base1)        Console.Write(solve(n, base1)+" ");} // Driver Codepublic static void Main(){    int n = 8;    printSumsOfDigits(n);}}// This code is contributed by Smitha
<?php// PHP program to find sum of digits of// n in different bases from 2 to n-1. // function to calculate sum of// digit for a given basefunction solve($n, $base){         // Sum of digits    $result = 0 ;         // Calculating the number (n) by    // taking mod with the base and adding    // remainder to the result and    // parallelly reducing the num value .    while ($n > 0)    {        $remainder = $n % $base ;        $result = $result + $remainder ;        $n = $n / $base;    }         // returning the result    return $result ;} function printSumsOfDigits($n){         // function calling for    // multiple bases    for ($base = 2 ; $base < $n ; ++$base)    {        echo(solve($n, $base));        echo(" ");    }} // Driver code$n = 8;printSumsOfDigits($n); // This code is contributed by Ajit.?>
<script> // JavaScript program to find sum of digits of// n in different bases from 2 to n-1.     // function to calculate sum of    // digit for a given base    function solve(n , base) {        // Sum of digits        var result = 0;         // Calculating the number (n) by        // taking mod with the base and adding        // remainder to the result and        // parallelly reducing the num value .        while (n > 0) {            var remainder = n % base;            result = result + remainder;            n = parseInt(n / base);        }         // returning the result        return result;    }     function printSumsOfDigits(n) {        // function calling for multiple bases        for (base = 2; base < n; ++base)            document.write(solve(n, base) + " ");    }     // Driver Code             var n = 8;        printSumsOfDigits(n); // This code contributed by Rajput-Ji </script>
Output : 
1 4 2 4 3 2 
 
Smitha Dinesh Semwal
jit_t
manishshaw1
sanskar27jain
Rajput-Ji
base-conversion
number-digits
Mathematical
School Programming
Mathematical
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Algorithm to solve Rubik's Cube
Merge two sorted arrays with O(1) extra space
Program to print prime numbers from 1 to N.
Find next greater number with same set of digits
Segment Tree | Set 1 (Sum of given range)
Python Dictionary
Reverse a string in Java
Arrays in C/C++
Introduction To PYTHON
Interfaces in Java