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A299199 In factorial base, any rational number has a terminating expansion; hence we can devise a self-inverse permutation of the rational numbers, say f, such that for any rational number q, the representations of q and of f(q) in factorial base are mirrored around the radix point and q and f(q) have the same sign; a(n) = f(1/n). 1
1, 4, 14, 98, 2, 4386, 18, 324, 60, 36457092, 12, 5769254382, 2598, 78, 414, 335391687123174, 510, 115428139222691670, 30, 1926, 20204166, 24752828962220504429646, 6, 1032336, 3124309416, 149376, 3816, 8542182056001396008878674488976, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

See A299161 for additional comments about f.

This sequence corresponds to the indices of ones in A299161.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 2..456

Wikipedia, Factorial number system (Fractional values)

Index entries for sequences related to factorial base representation

Rémy Sigrist, Colored logarithmic scatterplot of the first 5000 terms (where the color is function of A299160(n))

FORMULA

A034968(a(n)) = A276350(n) for any n > 1.

A299160(a(n)) = n for any n > 1.

A299161(a(n)) = 1 for any n > 1.

EXAMPLE

The first terms, alongside the factorial base representations of a(n) and of 1/n, are:

  n    a(n)         fact(a(n))                fact(1/n)

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

   2            1                         1   0.1

   3            4                       2 0   0.0 2

   4           14                     2 1 0   0.0 1 2

   5           98                   4 0 1 0   0.0 1 0 4

   6            2                       1 0   0.0 1

   7         4386               6 0 2 3 0 0   0.0 0 3 2 0 6

   8           18                     3 0 0   0.0 0 3

   9          324                 2 3 2 0 0   0.0 0 2 3 2

  10           60                   2 2 0 0   0.0 0 2 2

  11     36457092      10 0 4 1 3 5 0 2 0 0   0.0 0 2 0 5 3 1 4 0 10

  12           12                     2 0 0   0.0 0 2

  13   5769254382  12 0 5 8 4 5 2 1 4 1 0 0   0.0 0 1 4 1 2 5 4 8 5 0 12

  14         2598               3 3 3 1 0 0   0.0 0 1 3 3 3

  15           78                   3 1 0 0   0.0 0 1 3

  16          414                 3 2 1 0 0   0.0 0 1 2 3

PROG

(PARI) a(n) = my (v=0, q=1/n); for (r=2, oo, q *= r; v += floor(q) * (r-1)!; q = frac(q); if (q==0, return (v)))

CROSSREFS

Cf. A034968, A052126, A276350, A299160, A299161.

Sequence in context: A190481 A316414 A268689 * A209322 A110302 A282617

Adjacent sequences:  A299196 A299197 A299198 * A299200 A299201 A299202

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Feb 04 2018

STATUS

approved

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Last modified February 19 00:35 EST 2020. Contains 332028 sequences. (Running on oeis4.)