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Title: Sum of digits
Post by: cameyo on June 03, 2019, 12:55:27 AM

Given a number n, find the sum of its digits until sum becomes single digit.

Code Select Expand
Example: n = 7865 = 7 + 8 + 6 + 5 = 26 ==> 2 + 6 = 8

Code Select Expand
(define (digitSum n)
  (if (zero? n) 0
    (if (zero? (% n 9)) 9
      (% n 9))))

(digitSum 236753647864)
;-> 7

Title: Re: Sum of digits
Post by: rickyboy on June 03, 2019, 03:35:21 AM

Getta via il 9. :) https://en.wikipedia.org/wiki/Casting_out_nines

Title: Re: Sum of digits
Post by: cameyo on June 03, 2019, 03:49:49 AM

Yes, rickyboy. A very elegant solution.

Thanks for the italian translation :-)

Title: Re: Sum of digits
Post by: TedWalther on June 03, 2019, 01:17:22 PM

Code Select Expand

(define (digital_root n)
    (+ 1 (% (- n 1) 9))

> (digital_root 236753647864)
7

I heard this referred to as Raman's forumula, but not sure if that is the proper name for it. Even Wolfram's website didn't give an origin for it that I could find. It works though. I tested it on the numbers from 0 to 100.

Update:

I can't verify this, but further web searching indicates this solution may be a special case of Ramanujan's Congruence.

Title: Re: Sum of digits
Post by: cameyo on June 04, 2019, 11:19:09 AM

Some proofs:

//https://www.quora.com/How-would-I-prove-that-every-positive-integer-is-congruent-to-the-sum-of-its-base-10-digits-modulo-9

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Forum => newLISP in the real world => Topic started by: cameyo on June 03, 2019, 12:55:27 AM