

A294168


Irregular triangle read by rows in which row n contains significant digits after the radix point for unit fractions 1/n expanded in factorial base.


5



0, 1, 0, 2, 0, 1, 2, 0, 1, 0, 4, 0, 1, 0, 0, 3, 2, 0, 6, 0, 0, 3, 0, 0, 2, 3, 2, 0, 0, 2, 2, 0, 0, 2, 0, 5, 3, 1, 4, 0, 10, 0, 0, 2, 0, 0, 1, 4, 1, 2, 5, 4, 8, 5, 0, 12, 0, 0, 1, 3, 3, 3, 0, 0, 1, 3, 0, 0, 1, 2, 3, 0, 0, 1, 2, 0, 2, 3, 6, 8, 9, 0, 9, 2, 7, 0, 16
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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 p = p  1 for p prime.


LINKS



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



STATUS

approved



