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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, 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
Sequence in context: A190481 A316414 A268689 * A209322 A110302 A282617
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 04 2018
STATUS
approved

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Last modified July 20 09:18 EDT 2024. Contains 374445 sequences. (Running on oeis4.)