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 A269984 Numbers n having factorial fractility A269982(n) = 2. 7
 4, 5, 8, 9, 12, 14, 16, 18, 22, 23, 24, 26, 27, 32, 33, 37, 38, 39, 48, 49, 53, 54, 57, 58, 61, 64, 66, 78, 81, 83, 86, 87, 96, 97, 101, 107, 113, 114, 121, 129, 131, 139, 163, 169, 174, 178, 181, 193, 218, 227, 241, 257, 263, 267, 277, 302, 317, 327, 331 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A269982 for a definition of factorial fractility and guide to related sequences. LINKS Robert Price, Table of n, a(n) for n = 1..67 EXAMPLE NI(1/5) = (2, 3, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 3, 2, ...) NI(2/5) = (2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...) NI(3/5) = (1, 2, 3, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 3, ...) NI(4/5) = (1, 1, 2, 3, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, ...) so that there are 2 equivalences classes for n = 5, and the fractility of 5 is 2. MATHEMATICA A269982[n_] := CountDistinct[With[{l = NestWhileList[          Rescale[#, {1/(Floor[x] + 1)!, 1/Floor[x]!} /.             FindRoot[1/x! == #, {x, 1}]] &, #, UnsameQ, All]},       Min@l[[First@First@Position[l, Last@l] ;; ]]] & /@     Range[1/n, 1 - 1/n, 1/n]]; (* from Davin Park, Nov 19 2016 *) Select[Range[2, 500], A269982[#] == 2 &] (* Robert Price, Sep 19 2019 *) PROG (PARI) select( is_A269984(n)=A269982(n)==2, [1..300]) \\ M. F. Hasler, Nov 05 2018 CROSSREFS Cf. A000142 (factorial numbers), A269982 (factorial fractility of n); A269983, A269985, A269986, A269987, A269988 (numbers with factorial fractility 1, 3, ..., 6, respectively). Cf. A269570 (binary fractility), A270000 (harmonic fractility). Sequence in context: A042948 A126001 A321333 * A188085 A316097 A206554 Adjacent sequences:  A269981 A269982 A269983 * A269985 A269986 A269987 KEYWORD nonn AUTHOR Clark Kimberling and Peter J. C. Moses, Mar 11 2016 EXTENSIONS Edited by M. F. Hasler, Nov 05 2018 STATUS approved

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Last modified October 15 07:56 EDT 2019. Contains 328026 sequences. (Running on oeis4.)