Template:Sequence of the Day for October 9

Intended for: October 9, 2011

Timetable

• First draft entered by Alonso del Arte on August 7, 2011 ✓
• Draft reviewed by Mitch Harris on August 9, 2011 ✓
• Draft approved by Daniel Forgues on October 8, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

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A010888: Base 10 (additive) digital root of

n, n   ≥   0

.

{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, ... }

Repeatedly add digits of

n

until reaching a single digit. For the most part, in this procedure, 0s and 9s can be ignored (unless of course the number consists entirely of a 0 or several 9s; in the latter case the digital root is 9).

The (additive) digital root has the property

d r (n)  ≡  n  (mod 9),

which allows us to find whether

n

is divisible by 3 or 3 2 without doing any division (using a table).