A299020 a(n) is the maximum digit in the factorial base expansion of 1/n.

1, 1, 2, 2, 4, 1, 6, 3, 3, 2, 10, 2, 12, 3, 3, 3, 16, 4, 18, 1, 4, 6, 22, 1, 7, 9, 5, 5, 28, 4, 30, 4, 7, 9, 4, 3, 36, 13, 8, 3, 40, 5, 42, 8, 4, 15, 46, 3, 11, 6, 12, 9, 52, 6, 8, 6, 15, 15, 58, 2, 60, 22, 5, 6, 7, 9, 66, 12, 17, 4, 70, 4, 72, 31, 5, 14, 7

Offset

1,3

Comments

See the Wikipedia link for the construction method of 1/n in factorial base.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored scatterplot of the first 25000 terms (where the color is function of A052126(n))

Wikipedia, Factorial number system (Fractional values)

Index entries for sequences related to factorial base representation

Formula

a(n!) = 1 for any n >= 0.

a(n! / k) = k for any n > 1 and k = 1..n-1.

a(p) = p - 1 for any prime p.

Example

The first terms, alongside 1/n in factorial base, are:
  n     a(n)      1/n in factorial base
  --    ----      ---------------------
   1       1      1
   2       1      0.1
   3       2      0.0 2
   4       2      0.0 1 2
   5       4      0.0 1 0 4
   6       1      0.0 1
   7       6      0.0 0 3 2 0 6
   8       3      0.0 0 3
   9       3      0.0 0 2 3 2
  10       2      0.0 0 2 2
  11      10      0.0 0 2 0 5 3 1 4 0 10
  12       2      0.0 0 2
  13      12      0.0 0 1 4 1 2 5 4 8 5 0 12
  14       3      0.0 0 1 3 3 3
  15       3      0.0 0 1 3
  16       3      0.0 0 1 2 3
  17      16      0.0 0 1 2 0 2 3 6 8 9 0 9 2 7 0 16
  18       4      0.0 0 1 1 4
  19      18      0.0 0 1 1 1 6 2 0 9 5 2 6 11 11 13 8 0 18
  20       1      0.0 0 1 1

Mathematica

a[n_] := Module[{m = 0, r = 1, f = 1/n}, While[f > 0, m = Max[m, Floor[f]]; r++; f = FractionalPart[f]*r]; m]; Array[a, 77] (* Jean-François Alcover, Feb 05 2018, translated from PARI *)

Prog

(PARI) a(n) = my (m=0, r=1, f=1/n); while (f>0, m = max(m, floor(f)); r++; f = frac(f)*r); return (m)

Crossrefs

Cf. A052126, A246359, A276350.

Sequence in context: A072211 A360825 A328925 * A343505 A365687 A014665

Adjacent sequences: A299017 A299018 A299019 * A299021 A299022 A299023

Keyword

nonn,base

Author

Rémy Sigrist, Jan 31 2018

Status

approved