A229024 a(n) is the minimum distance to n! for the sum-of-digits of any factorial.

0, 0, 0, 3, 3, 9, 27, 18, 0, 0, 9, 9, 0

Offset: 1

Author

Hans Havermann, Sep 11 2013

Keywords

• nonn
• base
• hard

Comments

One could talk of signed integers here: 0, 0, 0, +3, -3, +9, +27, -18, 0, 0, +9, +9, depending on whether the minimum sum-of-digits finds itself above (plus) or below (minus) n!. The problem with so doing is that there might exist some n for which a nonzero minimum distance is both plus and minus.

Zeros indicate where there are solutions in A228311.

List of solutions:

1! 0 (0, 1)

2! 0 (2)

3! 0 (3, 4)

4! +3 (9, 10, 12, 13)

5! -3 (30)

6! +9 (116)

7! +27 (541, 554)

8! -18 (3154, 3186, 3219)

9! 0 (21966)

10! 0 (176755)

11! +9 (1607130)

12! +9 (16305323)

13! 0 (182624820)

Examples

			The minimum distance to 4! is 3, given by the sum of digits for 9!, 10!, 12!, or 13!.
The minimum distance to 5! is also 3, given by the sum of digits of 30!.
		

Links

• Hans Havermann, Determination of a(11)
• Hans Havermann, Determination of a(12)
• Hans Havermann, Determination of a(13)

Crossrefs

Cf. A004152, A228311.

Extensions

a(13) from Hans Havermann, Nov 04 2013