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A229024
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a(n) is the minimum distance to n! for the sum-of-digits of any factorial.
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2
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0, 0, 0, 3, 3, 9, 27, 18, 0, 0, 9, 9, 0
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OFFSET
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1,4
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COMMENTS
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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)
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LINKS
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EXAMPLE
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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!.
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CROSSREFS
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KEYWORD
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nonn,base,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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