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 A299020 a(n) is the maximum digit in the factorial base expansion of 1/n. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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) 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: A069922 A072211 A328925 * A343505 A070306 A014665 Adjacent sequences:  A299017 A299018 A299019 * A299021 A299022 A299023 KEYWORD nonn,base AUTHOR Rémy Sigrist, Jan 31 2018 STATUS approved

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Last modified June 19 14:08 EDT 2021. Contains 345140 sequences. (Running on oeis4.)