Sum a number's digits until only one digit remain

Question

I want to iteratively calculate the sum of a number's digits, until the result contains only one digit. For example, when $n=67946$ we get:

$$6+7+9+4+6=32\space\to\space3+2=5\tag1$$

So, when $n=67946$ I must get $5$.

When $n=649134976$

$$6+4+9+1+3+4+9+7+6=49\space\to\space4+9=13\space\to\space1+3=4\tag2$$

So, when $n=649134976$ I must get $4$.

I wrote:

Total[IntegerDigits[n]]

But this only gives the first iteration of the sum of digits.

Answer 1

Clear[s, t, n]

t[n_] := NestWhileList[Total[IntegerDigits[#]] & , n, # > 10 &]

---

Test:

t[649134976]

{649134976, 49, 13, 4}

If you don't want the interim values, use NestWhile.

---

A slight variation:

s[n_] := FixedPointList[Total[IntegerDigits[#]] & , n]

Test:

s[649134976]

{649134976, 49, 13, 4, 4}

If you don't want the interim values, use FixedPoint.