## sum_digits

Version 1.0.0.0 (1.54 KB) by
Find the sum of digits of a vector and an interesting script that uses it

Updated 26 Feb 2014

This function was primarily motivated by the script. I saw an interesting mathematical fact that (17576)^(1/3) = 1+7+5+7+6 = 26 or the cube root equals the sum of the digits. So I decided to write a script that searched for numbers that satisfied this criterion for arbitrary nth roots. However, I needed an efficient method for calculating the sum of the digits and I could not find any answers that provided the necessary efficiency in MATLAB so I wrote the function. The key to its efficiency is the fact that it can handle a vector of numbers.
This allowed me to calculate the sum of the digits of 99,999,999 numbers in under a minute and was limited by the computer's memory, not computational power. The script works well for most values of n (but I am concerned with accuracy at very large values). The values for n=2,3,4 are in the screenshot.

Some other solutions:
(34012224)^(1/6) = 3+4+0+1+2+2+2+4 = 18
(248155780267521)^(1/8) = 2+4+8+1+5+5+7+8+0+2+6+7+5+2+1 = 63
(196715135728956538880)^(1/10) = 1+9+6+7+1+5+1+3+5+7+2+8+9+5+6+5+3+8+8+8+0 = 107

%----------------------------------------------
% sum_digits.m
% Computes the sum of the input vectors digits
%----------------------------------------------
% dsum = sum_digits(x)
% x : vector of values
% dsum : vector of digit sums
%----------------------------------------------
% Example
% [7 6 10] = sum_digits([43 6 235])
% 7 = 4 + 3
% 6 = 6
% 10 = 2 + 3 + 5
%----------------------------------------------

Related items:
- Submission 32047 is in script form and uses a slightly different algorithm
http://www.mathworks.com/matlabcentral/fileexchange/32047-find-sum-of-digits-in-a-number-like-4209=15
- numlib::sumOfDigits for the MuPAD Notebook Interface but not available in MATLAB
- Various answered questions on MATLAB Central

### Cite As

Daniel R. Herber (2023). sum_digits (https://www.mathworks.com/matlabcentral/fileexchange/45695-sum_digits), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2013b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Categories
Find more on Creating and Concatenating Matrices in Help Center and MATLAB Answers