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digit sum (Definition)

Given an integer $ m$ consisting of $ k$ digits $ d_1, \dots, d_k$ in base $ b$, let

$\displaystyle j = \sum_{i = 1}^{k} d_i,$
then $ j$ is the digit sum of $ m$. Iterating this operation on the digits of $ j$ until $ j < b$ gives the digital root or repeated digit sum of $ m$. The digit sum and digital root of a number are the same only if the additive persistence of the digital root is 1.



"digit sum" is owned by CompositeFan. [ owner history (2) ]
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Cross-references: additive persistence, number, digital root, operation, base, digits, integer
There are 4 references to this entry.

This is version 2 of digit sum, born on 2006-11-05, modified 2006-11-05.
Object id is 8525, canonical name is DigitSum.
Accessed 899 times total.

Classification:
AMS MSC: 11A63 (Number theory :: Elementary number theory :: Radix representation; digital problems)
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