digit sum

digit sum (plural digit sums)

1. (mathematics, of a positive integer) The sum of all digits.

   The digit sum of 517 is 5 + 1 + 7 = 13.

   • 2004, J. F. Humphreys, M. Y. Prest, Numbers, Groups and Codes, Cambridge University Press, →ISBN, page 49:

     Given an integer X written in base 10 (as is usual), compute the sum of the digits of X: call the result the digit sum of X. If the digit sum is greater than 9, we form the digit sum again. Continue in this way to obtain the iterated digit sum which is at most 9.

2. (mathematics, of a positive integer) the number obtained when repeatedly applying above described operation until arriving at a single-digit number.

   The digit sum of 517 is 4, since 5 + 1 + 7 = 13 and 1 + 3 = 4.

   • 2012, Kiran Parulekar, Amazing Properties of Squares & Their Calculations, Kiran Anil Parulekar, page 17:

     The definition is that to find the digit sum of any number, add all the digits in the number. If number is a one digit no. then stop else add all the digits in this new number. Continue this process till we get one digit number.

   • 2002, Paul Swan, Investigating Patterns in Number Relationships, R.I.C. Publications, →ISBN, page 1:

     Every number has a digit sum. The digit sum of 7 is seven. The digit sum of 62 is eight (6 + 2). The digit sum of 728 is also eight (7 + 2 + 8=17, 1 + 7 = 8). The digit sum of a number is found by adding all the digits in the number until a single digit is left.

Those sources that hold to the first definition may refer to the second concept as the iterated digit sum, repeated digit sum or digital root.