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Find digital sums and digital roots?

Geoffrey Marnell
Posted 8 years ago

Hi

I'm a newbie to Mathematica (having played with it for just three days), so apologies for what might seem a dumb question. I can't find anywhere (even in the Help) a function for calculating the digital sum and the digital root of an integer. I can do it programmatically, but surely there is a built-in function or command for these common digit-manipulation tasks. Cheers

Geoffrey Marnell
POSTED BY: Geoffrey Marnell
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Thanks Sander. Silly me. I searched the help for "Offset" and got nothing of relevance Clearly, I should have searched for Mod!! Cheers Geoffrey
POSTED BY: Geoffrey Marnell

Thank you Szabolcs, Paul and Sander. This all works perfectly. I am intrigued by "offset". The accompanying documentation doesn't explain how it affects mod calculations. It works, but it puzzles me. Cheers Geoffrey
POSTED BY: Geoffrey Marnell

it does explain it:

enter image description here

one just has to read it...
POSTED BY: Sander Huisman
Paul Cleary
Paul Cleary
Posted 8 years ago

Or for the digital root you could use

digitalroot[k_Integer] := Mod[k - 1, 9] + 1
POSTED BY: Paul Cleary

Mod accepts a third argument, making this easier:

digitalroot[k_Integer] := Mod[k, 9, 1]
POSTED BY: Sander Huisman

One way to implement these would be

digitalSum[k_Integer] := Total@IntegerDigits[k]

digitalRoot[k_Integer] := FixedPoint[digitalSum, k]

FixedPoint will repeatedly apply digitalSum until the result does not change. A more explicit implementation could use NestWhile, with a check on the number of digits. But this trick with FixedPoint makes the code shorter.
POSTED BY: Szabolcs Horvát
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