OFFSET
1,4
COMMENTS
See the Wikipedia link for the construction method of 1/n in factorial base. This version eliminates the 1/0! and 1/1! places, which are always 0.
By convention, row n = 1 contains {0}.
Length of row n = A002034(n) - 1.
Length of row p = p - 1 for p prime.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10384 (rows 1 <= n <= 250).
OEIS Wiki, Factorial numeral system
Wikipedia, Factorial number system (Fractional values)
EXAMPLE
Row n = 7 contains {0, 0, 3, 2, 0, 6} since these are the digits that appear after the radix point in the factorial base expansion of 1/7. The length of row 7 = A002034(7) - 1 = 6, the largest number in row 7 is A299020(7) = 6, and the sum of row 7 = A276350(7) = 11.
1/n expanded in factorial base appears below; this sequence includes numbers to the right of the radix point.
-- ---------------------- ---------- ----------
1 1.0 1 1
2 0.1 1 1
3 0.0 2 2 2
4 0.0 1 2 3 2
5 0.0 1 0 4 5 4
6 0.0 1 1 1
7 0.0 0 3 2 0 6 11 6
8 0.0 0 3 3 3
9 0.0 0 2 3 2 7 3
10 0.0 0 2 2 4 2
11 0.0 0 2 0 5 3 1 4 0 10 25 10
12 0.0 0 2 2 2
13 0.0 0 1 4 1 2 5 4 8 5 0 12 42 12
14 0.0 0 1 3 3 3 10 3
15 0.0 0 1 3 4 3
...
MATHEMATICA
Array[With[{s = NumberDecompose[1/#, 1/Range[#]!]}, Rest@ Drop[s, -LengthWhile[Reverse@ s, # == 0 &]]] - Boole[# == 1] &, 17] /. {} -> {0} // Flatten
CROSSREFS
KEYWORD
nonn,base,tabf
AUTHOR
Michael De Vlieger, Feb 10 2018
STATUS
approved