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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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)

Index entries for sequences related to factorial base representation

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.

   n    1/n in factorial base     A276350(n)  A299020(n)

  --    ----------------------    ----------  ----------

   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

Cf. A002034, A007623, A276350, A299020.

Sequence in context: A212357 A114525 A127672 * A299196 A227698 A166124

Adjacent sequences:  A294165 A294166 A294167 * A294169 A294170 A294171

KEYWORD

nonn,base,tabf

AUTHOR

Michael De Vlieger, Feb 10 2018

STATUS

approved

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Last modified August 20 20:28 EDT 2018. Contains 313927 sequences. (Running on oeis4.)