login
A229024
a(n) is the minimum distance to n! for the sum-of-digits of any factorial.
2
0, 0, 0, 3, 3, 9, 27, 18, 0, 0, 9, 9, 0
OFFSET
1,4
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)
EXAMPLE
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!.
CROSSREFS
Sequence in context: A176158 A083008 A268092 * A117976 A010098 A029857
KEYWORD
nonn,base,hard
AUTHOR
Hans Havermann, Sep 11 2013
EXTENSIONS
a(13) from Hans Havermann, Nov 04 2013
STATUS
approved