The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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