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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 (list; graph; refs; listen; history; text; internal format)
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)

LINKS

Table of n, a(n) for n=1..13.

Hans Havermann, Determination of a(11)

Hans Havermann, Determination of a(12)

Hans Havermann, Determination of a(13)

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

Cf. A004152, A228311.

Sequence in context: A176158 A083008 A268092 * A117976 A010098 A029857

Adjacent sequences:  A229021 A229022 A229023 * A229025 A229026 A229027

KEYWORD

nonn,base,hard

AUTHOR

Hans Havermann, Sep 11 2013

EXTENSIONS

a(13) from Hans Havermann, Nov 04 2013

STATUS

approved

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)